Bí quyết ôn luyện thi đại học đạt điểm tối đa vật lý tập 1 lê văn vinh part 1

ThS.

L EVAN VINH

G I A O V I E N C H U Y E N L U Y E N T H I D A I HOC

Bl QUYET ON LUYEN THI DAI HOC DAT DIEM TO'I DA

VAT L I
TAP 1
THEO TtfNG o n j Y f i N D 6

vA GiAi a n TI6T

Bien soon theo cau true de thi cua Bo Giao Due va Dao too
(Tdi ban tan thA nhcU c6 sita chSa va bo sung)
- Tuyen tap cac bai toan cd ban, hay la va kho
- Tong hgfp cac phiiang phap giai nhanh nhat khi lam bai trac nghiem
- Sach danh cho hoc sinh luyen thi Dai hoc - Cao dang

NHA AUAT BAN DAI H O C QUOC GIAH A NQI


NHr^ x u n r B A N D R I H O C O U O C c m Hf^ N O I
16 H d n g C h u o i - H a i B d TrUng - H d N p i
D i e n t h o a i : B i e n t a p - C h e b a n : (OA) 3 9 7 1 4 8 9 6 :
H d n h c h i n h : C04) 3 9 7 1 4 8 9 9 ; T o n g b i e n t a p : ( 0 4 ) 3 9 7 1 4 8 9 7

L a m g i de c6 d u o c d i e m 10 m o n Vat ly? De thoi, neu d o la d i e m 10 t r o n g t h i
tot nghiep. Vay t h i cao dang t h i sao! Co de n h u tren khong? N o i c h u n g la cung

Fax: (04) 3 9 7 1 4 8 9 9

k h o n g k h o l a m . The con d i e m 10 trong de t h i dai hoc t h i sao! C o k h o l a m

Chiu

trdch

nhiem

khong? T a i day chac nhieu ban da c6 cau tra l o i r o i ! D a so nhieu ban cho rang

xuat ban

dieu nay la qua k h o va k h o n g the l a m duac. T u y nhien ben canh d o cijng c6
Gidm

doc - Tong

bien

tap :

TS. PHAM THj TRAM

nhieu ban cho rang cijng k h o n g c6 g i kho l a m va hoan toan c6 the l a m dugc
neu CO n h i r n g b i quyet o n luyen t h i bo ich truoc k h i buoc vao p h o n g thi. C u o n

Bien

CONG TY KHANG VIET

Che ban
Trinh

sach nay la d a n h cho cac ban n h u the va ciang danh cho cac ban c6 nit.:-,i t i n la

THU LUYEN

tap

CONG TY KHANG VIET

bay bia

m i n h se l a m d u o c dieu m o n g uoc do. Co so de t i n vao dieu nay la t r o n g k h u o n
kho cua de t h i k h o n g c6 cau nao qua k h o n h u ben de t h i toan. Vay cai k h o 6
day la gi? D o chinh la t h o i gian l a m bai. T r o n g de t h i c6 tong cong 50 cau
n h u n g chi c6 90 p h i i t v i the chia ra t h i 1 cau chi c6 108 giay (1,8 p h i i t ) . Vay b i

Tong phdt

hdnh

vd dot tdc lien ket xuat ban:
C O N G T Y TNHH MTV
DjCH V g VAN HOA K H A N G V I | T

Dia ch?: 71 Dinh Tien Hoang - P.Da Kao - Q.1 - TP.HCM
Dien thoai: 08. 39115694 - 39105797- 39111969 - 39111968

Fax: 08. 3911 0880
Email: khangvietbookstore©yahoo.com.vn
Website: www.nhasachkhangvlet.vn

quyet nao d e g i a i bai toan k h o khan 6 tren?
Bi quyet d a u tien de c6 d i e m 10 la phai bie't phan loai cap d o cau hoi va sau
do de l a m truoc, k h o l a m sau.
Bi quyet t h u hai la phai lam duoc n h u n g cau k h o dugc p h a n loai 6 tren
trong thai gian cho phep. De l a m dugc dieu nay d o i hoi cac ban phai giai dugc
that nhieu bai tap va phai phan ra t u n g chuyen de cu the de bie't bai toan giai
quyet theo h u o n g nao. N h u vay de giai quyet cac bai tap thugc d a n g k h o nay
cho nhanh va c h i n h xac nhat la n h i i n g g i cuon sach l a m dugc. V i the'de thuc
hien dugc b i quyet t h u hai t h i can l a m dugc n h i i n g viec sau:
1. Su d u n g thanh thao m o i lien h? giira dao d o n g dieu hoa v o i chuyen dgng
tron deu va cong cu de l a m dugc viec tren chinh la vong tron lugng giac. K h i

SACH L I E N K E T

sir d u n g v o n g t r o n l u g n g giac, cac bai toan n h u ve pha, thai gian, quang

Bf Q U Y E T ON LUYEN THI DAI HQC DAT DIEM TOI DA VAT U -

d u o n g ... dugc giai quyet true quan de hieu va it t o n t h o i gian (thi trac nghiem

TAP 1

can dieu nay nhat).
2. Phai s u d u n g tot kien thuc h i n h hgc phang de t i m d o I o n cac dai l u g n g

M a so: 1 L - 5 3 1 D H 2 0 1 3

Ma so ISBN:

vecto. T r o n g c h u o n g dao d g n g co t h i can n a m va ap d u n g d u g c d i n h ly h a m so

978-604-934-857-0

In 2.000 cuon, kho 1 6 x 2 4 c m

sin va cosin de t i m bien d o va pha ban dau cua dao d g n g tong h g p . Ben

- •

c h u o n g d o n g dien xoay chieu la can nhat v i cac h i n h phang 6 day dugc ve t u

Tai: Cty TNHH MTV IN AN MAI THjNH DLfC

phuang phap vecta trugt. D e giai tot cac bai tap t r o n g c h u o n g nay p h u o n g

Dia c h i : 7 1 , Kha Van ^ a n , P. Hiep Binh Chanh, Q . Thu Dufc, TP. H o Chi M i n h
So xuat b a n : 2033 - 201 3/CXB/03 - 2 8 4 / D H Q C H N

ngay 31/12/2013.

Quyet d i n h xuat b^n so: 5 4 3 L K - T N / Q D - N X B D H Q G H N , cap ngay 31/12/2013
In xong va n o p lOu c h i e u quy I n a m 2 0 1 4

phap vecto t r u g t k h o n g the k h o n g bie't t o i .

'

3. Sir d u n g thanh thao may t i n h cam tay (Fx 570 ES hoac Fx 570 ES PLUS).
T r o n g t i n h toan b i n h t h u o n g ma cac ban k h o n g c6 thao tac n h a n h tir chie'c ma>
tinh thi se mat kha nhieu thoi gian. Ngoai ra, chirc nang ciia cac chie'c may t i n t


vugt

nay con
xa su mong dgi cua chiing ta, no c6 the giai
ne'u dua ve chedo phuc.

dugc

nhieu bai toan

^hdn

1:

DAD

B O N G CII^U HdA

V A CDN LAC L d

XO

LY T H U Y E T

4. Nam chac cau true de thi de on diing trpng tarn, khong lang phi thoi gian

I. D A O D O N G C O
1.
Thendolddaodongca?

on nhiing kien thiic khong ra thi. Ne'u cac ban hpc ben ban co ban hoac khong
muon hoc chuong chuyen dong ciia vat ran ben ban nang cao thi cac ban nen

Dao dpng co la chuyen dpng qua lai quanh mpt v i tri dac bi§t gpi la vj tri
can bang.

chQn ban co ban ma thi. De thi cho chiing ta chon mpt trong hai phan nhung
chiing ta nen chpn ngay tix dau l u y f n thi chii khong de vao phong thi moi

2, Dao dong tudn hodn

chpn. Ne'u cac ban chac chan chpn ban co ban (da sochpn ban nay) thi cac ban

-

Dao dpng tuan hoan la dao dpng ma trang thai chuyen dpng ciia vat
dupe lap lai nhu cij (vi tri cii va huang cu) sau nhiing khoang thoi gian
bang nhau.

-

khong hgc cac kien thiic sau: nguyen chuang chuyen dpng cua vat ran, nguyen

Dao dpng tuan hoan don gian nha't la dao dpng dieu hoa

chuong tix vi mo den vT mo. Khong hoc phan hieu ling Doppler, con lac vat ly>
cac bai toan ve mac hinh sao, tam giac trong dong dien xoay chieu 3 pha, cac
bai toan ve thoi gian dao dong, so dao dpng, quang duong vat dao dpng dupe
trong dao dpng tat dan, cac cong thiic Einstein trong chuong lupng t u anh

II. P H l / O N G T R I N H C U A D A O D O N G D I E U HOA

sang, cac bai toan ve thay doi chieu dai, thoi gian trong thuye't tuong doi, cac

1. Vtdu

bai toan giao thoa anh sang bang cac dung cu quang hpc. Cac phan nay chi ra

-

y

Gia su M chuyen dpng ngupc

chieu

ben ban nang cao v i the chiing ta phai loai bo ngay cac kien thiic nay de khong

duong van toe goc la co, P la hinh chieu

bi phan tam va mat thoi gian.

ciia M len Ox.

5. Nho cong thiic. Chiing ta khong the diing cong thiic nao ciing d i chiing

cot -fj

Tai thoi diem t = 0, M co tpa dp goc (p

minh ma tot nha't la trong qua trinh hpc hay chiing minh va nho no de lam bai

Sau thoi diem t, M co tpa dp goc (ro.t + cp)

t^p moi nhanh dupe.

Khi do: OP = x => diem P co phuong trinh la:

6. Phai biet tinh nham cac bieu thiic tinh co ban nhu cos—= 0;cos —= —...
2

3

2

nhfmg cai nay nham nhanh hon may tinh nhieu. Phai thanh thao may tinh cam
tay nhung dung de phu thupc vao no.
7. T u tin va kien tri on luy^n, nha't dinh cac ban se thanh cong.
Tac gia

X = OMcos(cot + (p)
-

Nhd Sdch Khang Viet xin trdn trgng gi&i thi^u tai Quy doc gid vd xin
lang nghe tnoi y kien dong gop decuoh sdch ngdy cdng hay han, boich han.

-

Email:

Do ham cosin la ham dieu hoa nen diem P dupe gpi la dao dpng dieu hoa
Dao dpng dieu hoa la dao dpng trong do l i dp ciia vat la mpt ham cosin
(hay sin) ciia thoi gian.

3. Phuong trinh
-

Phuang trinh x = A cos(co.t + (p) gpi la phuong trinh ciia dao dpng dieu hoa
*

(co.t + (p) la pha ciia dao dpng tai thoi diem t

*
4.

A la bien dp dao dpng va la li dp cue dai ciia vat. (A > 0).

*

Cty T N H H Mpt thanh vien - Dich V u Van Hoa Khang Vi?t.

Tel: (08) 39115694 - 39111969 - 39111968 - 39105797 - Fax: (08) 39110880

' '

2. Dinh nghia

ve:

71- D i n h Tien Hoang, Phuang Dakao, Qu|n 1, TP H C M .

Dat A = O M t a c 6 : x = Acos(co.t + (p)
Trong do A, w, c la hang so
p

Le Van Vinh

Thuxingtti

/

c la pha ban dau tai t = 0 ((p > 0;(p = 0;(p < 0)
p

Chuy

a) Diem P dao dpng dieu hoa tren mpt doan thang co the coi la hinh chieu
ciia diem M chuyen dpng tron deu len duong kinh la dogn thang do.


b) Ta quy uoc chon true x lam goc de tinh pha aia dao dong va chieu tang cua
pha tuong ling voi chieu tang ciia goc MOP trong chuyen dong tron deu.
I I I . CHU K I , T A N SO, T A N SO GOC CUA DAO D Q N G DIEU HOA
1. Chu ki va tan so
Khi vat tro ve vi tri cii, huong cii thi ta noi vat thuc hi^n 1 dao dong toan phan.

*

Tong luc tac dung len vat: F = -kx
•k
Theo dinh luat I I Niu ton: a =
x
m
Dat co^ = k/m => a + co^x = 0

Chu ki (T): ciia dao dong dieu hoa la khoang thai gian de vat thuc hien
mpt dao dong toan phan. Don vj la s

*

Neu keo vat khoi vj tri can bang va buong ra vat se dao dong quanh vi tri
can bang, gii>a hai vj tri bien
V I I . K H A O SAT DAO D Q N G CUA CON LAC LO XO VE M A T D Q N G
LI/C HQC
Xet vat 6 li dp x, 16 xo gian mot doan Al = x. Luc dan hoi F = - k A l

Tan so (f): cua dao dong dieu hoa la so' dao dong tuan hoan thuc hien
trong mgt s. Don vi la 1/s hoac Hz.
Trong dao dong dieu hoa o) dupe gpi la tan so goc.
Giiia tan so'goc, chu ki va tan so c6 moi lien he:

Tan so goc: (» = . —
m

= 27lf
T

IV. V A N TOC VA GIA TOC CUA DAO D Q N G DIEU HOA
1. Van toe

*
*

-

Van to'e eiing bie'n thien theo thoi gian

*

Tai

*

Tai

X

= ±A thi v

=

0

X = 0 thi V = vmax =

to.A

2. Gia toe
Gia to'c la dao ham ciia van to'e theo thoi gian
a = v ' = x" = -co^A cos(a)t + c}))
a = -LoH
*

Luc keo ve

Tai

M.

Luc huong ve vi tri can bang gpi la luc keo ve. Luc keo ve c6 dp Ion ti le
voi li dp va gay gia toe cho vat dao dpng dieu hoa.
V I I I . K H A O SAT D A O D Q N G CUAA LO XO VE M A T N A N G L l j Q N G
1. Dong nang cua con lac Id xo: W^j = ^ mv^
2. The nang eua con idc Id xo: Wt = - kx
-

. T
The'nang va dpng nang ciia con lac 16 xo bien thien dieu h6a voi chu ki —

3. Co nang eua con idc Id xo. Su bdo toan eo nang

Taix = Othia = 0

*

F

Chu ki:

Van toe la dao ham ciia l i dp theo thoi gian:
V = x' = -coA sin(a)t + cj))

.j't!:i

Vay dao dpng eiia con lac 16 xo la
dao dpng dieu hoa.

2. Tan so goc

CO =

'

X = ±A

thi a = am.ix = co^A

V. DO T H I CUA DAO D Q N G DIEU HOA
Do thi ciia dao dpng dieu
hoa vai cj) = 0 c6 dang hinh
sin nen nguai ta con gpi la
dao dpng hinh sin.
V I . CON LAC L 6 XO
Con lie 16 XO gom mot vat nang m gan vao 1 dau ciia 16 xo eo dp eung k
va khoi lupng khong dang ke. Dau eon lai eiia 16 xo eo dinh.
Con lac CO 1 v i tri can bang ma khi ta tha vat ra vat se dung yen mai.

2

2

2

2

Co nang ciia con lac ti le voi binh phuong voi bien dp dao dpng
Co nang ciia con lac 16 xo dupe bao toan neu bo qua mpi ma sat.
N h a n x e t q u a n t r o n g : dis'dat diem cao phan nay thi hi quyet dau tien la
cdc ban phdi su dung dwgc duang tron htgng gidc thuan thuc vd sau day la hi
quyet thu nhat.

' '''''

"'

5


S a u d a y l a p h u o n g phap khac rat t r y c quan, the hien d u g c mo'i q u a n he

Chuyen de 1

giira cac dai l u g n g n h a m g i i i p cac ban t r o n g vi#c giai n h a n h nha't, c h i n h xac
nha't cac dang toan ve dao d o n g co, song co, d o n g d i e n xoay chieu va dao

D U O N G T R 6 N LUgrNG GlAC TRONG DAO D O N G Bltu H6K

d g n g t r o n g mach L C . co the n o i rang: p h u o n g phap d i i n g d u o n g t r o n l u g n g

I. KHO KHAN KHI G I A I BAI TAP:

giac quye't d i n h I o n den viee dau hay rot ciia cac ban.

So l u g n g cong t h u c yeu cau cac ban n h o van d y n g t r o n g c h u o n g dao d g n g

II. PHl/CNG PHAP

CO rat n h i e u chi t i n h p h a n to d a m , bat bugc la 16 cong t h i i c n h u n g v o i so'

Bieu d i e n ca ba h a m l i d g (x), v a n toe

l u g n g cac cong thuc d o cung chi giai quye't d u g c cac cau h o i rat co ban,

(v) va gia toe (a) va k h i can ta co the

k h o n g the giai quye't d u g c he't cac dang bai tap dat ra cua c h u o n g nay. O

bieu d i e n lire tren c i i n g m g t d u o n g

phan dao d g n g kie'n thuc toan lien quan la cac cong t h u c l u g n g giac va giai
cac p h u o n g t r i n h l u g n g giac day la kho khan I o n do'i v o i da so' cac ban ke ca
cac ban kha g i o i v i ra't hay sot n g h i ^ m b o i t i n h lap lai cua h a m t u a n hoan.

t r o n l u g n g giac n h u sau:
+

L i dp: X = A cos(cot + cpx) la h a m cosin

D u o n g t r o n l u g n g giac v o i vi^c lien he giira chuyen d g n g t r o n deu v o i dao

=> c i i n g chieu true cosin co chieu (+)

d g n g d i e u hoa se giai quye't n h i i n g kho khan tren m o t each de dang.

tir trai sang p h a i v o i bien d g la => x^^^^ = A

H i e n tai tren d u o n g t r o n l u g n g giac da so' chi s u d u n g m o t true cosin cho

+

p h u o n g t r i n h dao d g n g x = A cos(cot + (p^) (true Ox) va cac dang toan c h u o n g

V a n toe tijfc thai: v = -A(osin(cot + cpx) la h a m trir sin
=> ngugc chieu true sin nen co chieu (+) h u o n g tir tren xuo'ng v o i bien d g

nay t h u o n g can c i i vao cac d\x kien bai toan cho t u p h u o n g t r i n h dao d g n g

v^ax^^-'^-

d a n g X = A cos(cot + (Px), de t i m chu k i , tan so', d u o n g d i , k h o a n g t h o i gian

D i e u nay

tuong duong

voi ham

v = Acocos(cot + (Pv)

voi

de d i t u toa d g xi den toa d o xi, t i m van toe, gia toe tai m g t t h o i d i e m nao
do, khoang t h o i gian 16 xo nen, gian ...
T u y nhien se kho khan cho cac ban k h i gap phai loai cau h o i dv! kien bai

+

G i a toe tuc thoi: a = -a)^Aeos((ot + cpx) la h a m trir cosin (ngugc h a m x)
=> ngugc chieu true cos co h u o n g (+) tir phai sang trai v o i bien d o a^^ =cf^A

toan k h o n g cho p h u o n g t r i n h dao d g n g dang l i do x = Acos((ot + cp^) ma
cho dang v a n toe tue t h a i v =-A(osin(cot + (Px)hoac cho d a n g gia toe tiic

D i e u nay t u o n g d u o n g v o i ham: a = a)^Aeos(cot + (Pa) v o i (pg = (p^, + ^ = (px + Ji

t h o i a = -(a'^Acos((ot + (Px) • Luc nay hau he't cac ban deu b i d g n g k h o n g the
bieu d i e n h a m (v) va h a m (a) tren d u o n g t r o n l u g n g giac.

T h o n g qua each bieu d i e n nay ta tha'y mpt so diem dac bi?t, vung dac biet

M u o n bieu d i e n d u g c tren d u o n g tron l u g n g giac t h i p h a i t u h a m (v), (a)

va m o i q u a n he ve pha ciia l i d g (x), van toe (v), gia toe (a) cung n h u viee

vie't lai d a n g h a m (x) bang each lay tich phan bac nha't h a m v a n toe (v) hoac

khai thae cac kien thuc l y thuye't lien quan ve dao d g n g dieu hoa, cac dang

bae 2 h a m gia toe (a) day la each rat kho k h a n cho cac bah v i sang hge k y 2

nang l u g n g ciia dao d g n g dieu hoa dugc the hien m g t each true q u a n tren

cac ban m d i d u g c hge n g u y e n h a m va tich phan. Vay giai phap nao c6 the

h i n h ve v o i m g t vai v i d u sau:

giai quye't cac k h o k h a n neu tren?

+

Bon vi tri dac biet:

N h i e u y kien cho r i n g : N e u m u o n tranh dieu nay t h i p h a i n h o h a m van toe

•

V i tri bien duong I: (x^^x = A ; v = 0; a = -co^A)
=> The'nang cue d a i , d g n g nang cue tieu

(v) som pha h o n l i d g (x) 1 goc ^ , con h a m gia to'c (a) ngugc pha v o i h a m l i
d g (x) t u y nhien, vi^c giai cac p h u o n g t r i n h l u g n g giac lien q u a n dieu nay
m a t n h i e u t h o i gian, chua m u o n noi d g chinh xac v o i da so cac ban la rat

-

V i tri can bang I I :

(x=0;

v = -coA;

a=0)

tha'p. K h o n g the n h o he't cac cong thuc, cac m o i quan he p h u c tap cua cac
dai l u g n g co hge, v i thie'u t i n h true quan, thie'u m o i q u a n h ^ gSn bo giira cac
h i ^ n t u g n g vat ly nen t h u o n g tra l o i sai cac cau h o i d u co ban nha't.
6

=> The'nang cue tieu, d o n g nang eye dai
V i tri bien am I I I :
(x = - A ; v = 0 ;

a^^^x =co^A)


I I I . CAC DANG TOAN
D a n g l : X a c d j n h c a c dai lUcfng li do, v a n toe, g i a t o e t a i thdi
d i e m t.

=> T h e n a n g cue dai, d o n g nang cue tieu
-

V j t r i can b i i n g I V : ( x = 0 ;

v^-,^=wA;

a = 0)

=> Tlie'nang cue tieu, d o n g nang cue dai
Kei luan: Vay dm ki dao dgn^ titan hoan cua ham dgn^ nang va ham thenang

cua

dao dong dieu hoa chi bang ^ chu ki T cua ham li do (x), khodng thai gian dedong
nang (the nang) tie cur dai thanh cite tieu hay ngugc lai la ~ chu ki T cua ham li

ga v i DU MAU:
V I d u 1 : M o t vat dao d o n g dieu hoa theo p h u o n g t r i n h x = 6eos(27tt)cm,
van toe ciia vat tai t h o i d i e m t = 7,5s la:
A. V = Ocm/s.

B. v = 75,4cm/s.

C. V = -75,4cm/s.

D . v = 6cm/s.

^hdn tich vd huong ddn gidi

do (x).
+

.. t\.

Bon vung dae biet:

II

D u n g true Ox bieu dien :

V u n g l : (x>0;

lue ban dau vat 6 v j t r i I sau t h o i gian

v < 0; a < 0)

=> vat chuyen d o n g nhanh dan theo chieu (-) v i a.v > O v a the nang giam,

t = 7,5s vat quay m o t goc:

d o n g nang tang.

cot = 271.7,5 = 1571 lap lai 7,5 v o n g

V u n g 2: (x < 0; v < 0; a > 0)

den v i t r i I I I => co van toe v = 0.

=> vat chuyen d o n g cham dan theo chieu (-) v i a . v < 0 va the nang tang,

C h p n dap an A

a

o

IV

d o n g nang g i a m .
V u n g 3: (x < 0 ;

V

v > 0; a > 0)

=> vat chuyen d o n g nhanh dan theo chieu (+) v i a.v > 0 va the nang giam,
d o n g nang tang.
V u n g 4: ( x > 0 ;

v>0;

A . a = Ocm/s2

d o n g nang g i a m .
Mo'i quan he vepha eua li do (x), van toe (v),gia toe (a): Qua h i n h ve nhan
tha'y d u g c m o i quan he ve pha ciia ham l i do (x), van toe (v) va gia toe (a) la:
9v

=
+

va

m o t goc

va tre pha h o n gia toe (a)

^

=> gia toe (a) som pha h o n van toe (v) m o t goc ^ va s o m pha h o n l i do (x)
m o t goc 7t hay ngugc pha v o i l i do (x)

2y

cm.

B. a = 946,5em/s2.

C. a = -947,5cm/s2

D . a = -946,5cm/s2.

'Phdn tich vd hu&ng ddn gidi
D i i n g true Ox bieu dien
De cho h a m x dang sin can

chuyen

sang cos c6 dang: x = 6cos(47it) cm

(Pa = (p^ + ^ - (p, + 71

=> van toe (v) sam pha han l i d o (x) m o t goc

Vl d u 2: M o t vat dao d o n g dieu hoa theo p h u o n g t r i n h x=6sin
gia toe ciia vat tai t h o i d i e m t = 5s la:

a < 0)

=> vat chuyen d o n g cham dan theo chieu (+) v i a . v < 0 va the nang tang,
+

;

=> ban dau vat 6 v j t r i I sau thoi gian
t = 5s vat quay 1 goc o)t - 4n.5 - 20n
lap lai 10 v o n g den v j t r i cij.
=> CO gia toe a = -co^A = - 9 4 7 , 5 ^
s
C h g n dap an C
Vl d u 3 : M o t chat d i e m dao d o n g dieu hoa theo t c6 p h u o n g t r i n h van toe
v = 107reos 27rt + - em/s, toa dp ciia chat d i e m tai thoi d i e m t = 1,5s la
V
2J
_ A . x = l,5cm.

B. x = -5em.

C. x= + 5cm.

D . x = 0cm.
9


Cty n V H H M T V D W H JOtang

'Phdn tich vd hitang dan gidi

Bl/ofC 3 : Bieu d i e n dao d p n g dieu hoa tren d u o n g t r o n . Vat d i tir v i t r i X j

= 5cm

Bien d p A =
CO

den X2 t u o n g u n g v o i m p t chuyen d p n g t r o n deu d i tir M deh N v a i v a n

271

D u n g true O v bieu d i e n :

toe goc CO, ban k i n h la A .

L i i c ban d a u vat a v i t r i I sau t h o i gian

CO

= - A = - 5cm.

m

C h p n dap an B
Vl d u 4 : Van toe cua m p t vat dao d o n g d i e u hoa bien t h i e n theo t h o i gian
theo p h u o n g t r i n h v = 27:cos 0 , 5 7 : t - - (cm/s). Vao t h a i d i e m nao sau
6y

v i DU

Vi d u

MAU:

1 : Vat dao d p n g d i e u hoa v o i p h u o n g t r i n h x = Acos(cot + cp) (cm).

T i n h t h a i gian ngan nhat vat d i t u :
A
a) V j t r i can bang den v i t r i x = — .

day vat qua v i t r i c6 l i d p x=2cm theo chieu d u o n g cua true tpa d p .
A.8/3S

B.2/3S
^hdn

Bien d o A = ^ ^

CO

= — =

0,5Tt

C. 2s

D . 4/3s

tkh vd hii&ng dan gidi
4cm

b) V i t r i can bang den v i t r i x =
c) V j t r i can bang den v j t r i x =

^hdn
(POv

sau t h a i gian t v a t quay 1 goc

AV2

2
A^f3

d) V j t r i can bang den v i t r i x = A .

D u n g t r y c O v bieu d i e n :
Luc ban d a u vat 6 v i t r i V

. .,;.

=> T h a i gian v a t d i t u v i t r i X j den X2 la : At = — .

lap lai 1,5 v o n g den v i t r i I I I
X

«,

Slide 4 : Xac d j n h goc cp = M O N .

t = 1,5s vat quay 1 goc cot = 2 i i . l , 5 = 3n

=> CO toa d o

tich vd hu&ng ddn gidi
A

=-7

a) K h i vat d i tir v j t r i can bang den ^ = y ,

o
^Ov =

t u o n g u n g v o i vat chuyen

d p n g tren

d u o n g t r o n t u M den N d u o c m p t goc

a = cot = 0,57rt = — v i c6 l i d p x = 2cm,
3

Acp n h u h i n h ve ben.

bien d p A = 4 cm va c h u y e n d o n g theo chieu {+) den v j t r i V I

De thay: sin Acp = ^ => Acp =

=> mat t h o i gian t = 2/3s. C h g n dap an B

=> K h o a n g t h o i gian ngan nhat de vat d i t u

Dang 2: Xac d j n h t h d i g i a n v a t d i tuT vj t r i x j den v i t r i x j :
Phi/cTng p h a p g i a i :
Cho p h u o n g t r i n h dao d p n g vat c6 dang:
X = Acos(cot + (p)cm

BUdc 1 :

Xac d i n h v j t r i X j tren d u a n g

Bl/dc 2:

Vj<0;

hay

10

>0;

Xac d i n h v j t r i X2 tren d u o n g
V2

<0;

la: At =

CO

d p n g cua

hay V2 = 0 ) .

AV2

rad.

n
6

T

27t

12

T
bang

den

^
,
-, t u o n g u n g v o l vat chuyen

Vi=0).

t r o n va chieu chuyen
(V2

VTCB deh X = 2

Acp

b) K h i vat d i tir v i t r i can

t r o n va chieu chuyen d p n g ciia vat
(v;>0;

Vift

vat

^

d u p e m p t goc Acp n h u h i n h ve ben.
De thay: sin Acp = — => Acp = - rad.
2
4
^

V

I—

=i> K h o a n g t h o i gian ngan nhat de vat d i t u VTCB deh x = — — la:


Bi qtiyei on luyen thi dai hoc dat diem toi da Vat It, tap l~Le

At =

Van Vinh

Cty TNHH MTV DWH

Tit hang nay, ta sc gicii qiii/ct nhi'mg bai tocin vc thai gian trong dao dong dieu hoa
mot each nhanh nlid't neii dccho diem di va diem den dqc bict nhu tren.

Acp
CO

8

2n
T

c) K h i vat d i tir v i t r i can b^ng den x =

BAI TAP VAN DUNG:

p
, t u o n g l i n g v a i vat chuyen dpng

tren d u o n g t r o n t u M den N duoc m o t goc Acp n h u h i n h ve ben.

C a U 1: Vat dao d o n g dieu hoa v o i p h u o n g t r i n h x = Acos(cot + cp) (cm). T i n h :
a)

Thoi gian ngan nhat vat d i t u v i t r i c6 l i do X| =

vat d i t u V T C B den x =

At =

Acp
C
O

n
_3_
2n

I

• •
A

b) Thoi gian ngan nhat vat d i tif v i t r i c6 li do

la:

X2 =

6

t u o n g u n g vcVi vat chuyen d o n g tren

theo chic?Li am.

d) Thoi gian ngan nhat vat di tir vj t r i ccS l i dc) x, = -A

d u o n g t r o n t u M den N d u o c m o t goc
Acp n h u h i n h ve ben.

X2 =

AV2

den vj t r i c6 l i dc>

theo chieu am.

De thay: sin Acp = ^ => Acp = ^ rad.

'Phdn tick vd huang dan gidi
a) Khoang t h o i gian ngan nhat vat d i tir

=> K h o a n g t h o i gian ngan nhat de
vat d i t u V T C B den x = A la:

vi t n X, =

AV3

—

A

den ^2 = y

tuong

u n g vc>i vat chuyen dcing tren d u o n g

_^

^

tron tir M den N .

CO

Min t
T o m lai: ta c6 bang thoi gian trong dao dong dieu hoa sau:

-A

den v i t r i c6 l i dc)

A

X-, =

d) K h i vat di t u v i t r i can bang den x =

2

^\ —

' 2 •
AN/2 den vj t r i c6 li do
c) Thoi gian ngan nhat vat d i tir v i t r i c6 l i do x, = - ~ ^
2
Av'3

T

Acp
At = -

den v i t r i c6 l i do

A

V3

Acp = — rad.
^
3
=> K h o a n g t h o i gian ngan nhat de

De thay: sin Acp =

Khang Viet

o

(
2

A
2

= t

Asfd.

=1
~ 6^
T_
12

>0

+ t,

0-^

2 ;

L-1
4

Ta bieu dien cac d i e m tren len true dao d o n g dieu hoa se thay ro h o n

T

~A

_AS

A42 _A

o

\

T_
6

•1

L
4

^

]

r

* '

A

Ayll A41

T
12

4
1 -x


Bf quyei on liiyen ilii dai hoc dat diem tot da Vat It, t^p 1-Le Van Vitth

d) Khoang thoi gian ngSn nha't v^t di tu vj
tri xi = - A den xj =
theo chieu

b) Khoang thoi gian ngan nha't vat di tij" vi
A ^
tri X j A
— dpng = - dirong tron tix M
vat chuyen den X2 tren — tuong img voi
den N.
Min t (A A' = t
+ t 0-+
>0
I2 >—
2,

I2

y

am tuong u n g voi vat chuyen dong tren
-A
d u o n g tron tu M den N.
^
AV2 ^ = t(~A->0) + t(O^A) + V
Aj2]
A—•—•—

2

I

T

4

~ 12 ^ 1 2 " 6
Bieu dien len tryc dao dong dao dgng dieu hoa

-A

O

T_

12

T

= —+ — +

A
2

L2
1

Ayfl AS

A^

A-Jl

fT

T\

4 U

8

_A

5T

A

A-JIAS

6
Tdi day ta da cd cdi nhin mai vedang todn th&i gian trong dao dong
dieu hoa, tif day ede bai vequdng duang, toe do trung binh, van toe trung binh... eo
the dime gidi qiiyet rat de dang.
Ket luan:

c) Khoang thoi gian ngan nha't vat di tvr vi tri
xi = A>/2 den X2 = A V 3—
-y
theo chieu am tuong ung voi vat chuyen
dong tren d u o n g tron tu M den N.
+ t(O^A) + t
A>/2 A 7 3 1 = t

D a n g 3. B a i t o a n x a c d j n h t h d i d i e m v a t d i q u a v j t r i x d a b i e t
( h o $ c V, a, \Nt, Wd, F) I a n thuT N
PHl/QNG P H A P

* Trong mot chu ky T (27r) vat di qua x hai Ian neu khong ke den chieu
chuyen dpng, neu ke den chieu chuyen dong thi se di qua 1 Ian
* Xac dinh Mo dua vao pha ban dau (xo, vo chi quan tarn < 0 hay > 0 hay = 0)
* Xac dinh M d u a vao x (hoac v, a, Wi, WJ, F )

2 -

= 1 I fl_ll I I T

12
Bieu dien len true dao dong dieu hoa

-A

A42 A

^V3

T

8

O

A
2

A-Jl

A(p

Ap d u n g cong thuc t = (0
V
Liru y: De ra thuong cho gia tri n nho, con neu n Ion thi tim quy luat de
suy ra nghiem t h u N.
^
T
6

T
4

Thai gian dao dong cua vat dugc xdc dinh nhu a tren nhimg hinh ve duai eho edc
ban CO cdi nhin true quan hem

Cdc loai thucmggap vd cong thiic tinh nhanh

- Q u a X k h o n g ke den chieu

+ N chin: t = ^ ^ ^ T + t2 i h ^hoi gian de vat di qua vi tri x Ian thu 2 ke tu
thoi diem ban dau)

15


Bi 4ityet on luySn thi aai ntfcflflfaiem TOi aa var ii, lup I-LB

+

N le: t =

N - 1

van

vmn

T + t i (ti t h a i gian de vat d i qua v i t r i x Ian t h u 1 ke t u t h a i

N h ^ n xet: each tinh theo cac khoang thoi gian dqt Met tuy trinh bay tren giay thdy
nhieu ban nhung thuc tetinh thi rd't nhanh. Khi gidi chiing ta khong can ghi cu the

d i e m ban d a u )
-

md chi viec cong cdc khodng thai gian Iqi thoi.

Q u a X ke den chieu (+ ho|c - )

Cung bdi todn tren nhung neu thai diem di qua vat Id rdi l&n thi ta lam nhu vi du sau

t = ( N - 1)T + t j ( t i t h o i gian de v a t d i qua v i t r i x theo chieu d a u b a i quy
d i n h Ian t h i i 1 ke t u t h a i d i e m ban dau)

m vi D U
V I dy

V l dM 2: M p t v a t dao d p n g dieu hoa v o i p h u o n g t r i n h x = 4cos(47tt + — )cm.
6
T h o i d i e m t h u 2013 vat qua v i t r i x = 2cm.

1 : M p t v a t dao d o n g dieu hoa v o i p h u a n g t r i n h x = 4cos(47it + —)
6

c m . T h o i d i e m t h u 3 v a t qua v i t r i x = 2cm theo chieu d u a n g .
A.9/8S

B. l l / 8 s

C.5/8S

^- -IT'

D . 1,5 s

Cach 1 : G i a i theo p h u o n g trinh lugrng giac

Ta CO

lv>0^1

V = -167tsin

7l^
47rt+-

6J

>0

3

t = A + ii (keN)
24
2 ^
'

47ct + - = — + k27t
6
3

= > 4 7 t t + - = — + k27t

6

D . D a p an khac

'Phdn txch vd huang ddn gidi

47tt + — = - + k27:
6
3

x= 2

x = 4cos 4 7 r t + - = 2
6

^ 24157
C.
s
24

27T
271
1, ,
s)
C h u k y dao d o n g : T =: — = — = -- ((s)
CO
47t
2
CO

47t
Cach 1 : G i a i theo p h u a n g trinh lugtig giac

'Phdn txch vd huang dan gidi

x=2

^ 12061
B.
s
24

12073

MAU:

t = - i + Ji ( k e N * )
8
2^
'

T h o i d i e m t h u 2013 (le) nen ta d u n g cong thuc: t =

= > t = - — + — k e N . T h o i d i e m t h u 3 l i n e v o i k = 3=> t = —s
8 2
^
8

N-1

T + ti

V o i ti la t h o i gian de v a t d i qua v i t r i x = 2cm Ian t h u 1 ke tir t h o i d i e m ban
dau u n g v o i k = 0 (nghiem tren).

C a c h 2 : S u d\ing d u o n g tron luQmg giac
Pha ban d a u (p = — nen ban d a u v a t 6 v i t r i M Q . V a t qua x = 2 c m theo chieu

,
Vay t i =

d u o n g la qua M 2 . Q u a M 2 Ian t h u 3 u n g v o i vat quay d u g c 2 v o n g (2T)

Vat qua v j t r i x = 2cm Ian t h u 2013 la :

6

(qua 2 Ian) v a Ian cuoi cung d i t u M Q den M 2 .
Goc quet A(p = 2.2n +

3n

^

^

t=

t=^=Hs

8
Hoac t i n h theo cac khoang t h o i gian dat biet:
XMO

=

4V3
AV3 .
o
4
A
^ = - r - v a XM2 = 2 = - - 2
2

tM o ^ M 2 -VA../3
= 1 +1
6

I

(O^-A) + '(-A^O)

T _3T_3.0,5_3

4 ^ 4 ^ 1 2 "

4

~

4

+t

X

-A f

A

1

0

1 . .

2

24

2

24

N-1 ^ ^
T + ti
2
"

=

2013-1 1
2

1

.- +— =
2^24

12073
24

Cach 2 : S u d v n g duong tron lupng giac
Vat qua x = 2 la qua M i va M 2 .

-A

Vat quay 1 vong (1 chu k y ) qua x = 2 la 2 Ian.
Qua Ian t h u 2013 t h i phai quay

A^
0-»—
2y

k

C h p n dap an A

Mo

C
O

1

24

— + - = — + - = —(s)

1006

v o n g r o i d i t u M o den M i .
M2

Goc quet Acp = 1006.271 + ^

.~8

^ t . 2 T . ^ , M = ll(s)?«^^''*-;

CO

24

24

T { ^ ' ; V;£f^ TiivH BiNH Vvwim

C h p n dap an A
16

17


Cty TNHHMTV

2 2

.2 -^0

T j r __T
6

12~12

T
0 5
12073
t = 1006T+ — = 1006.0,5+ — = - ^ = ^ s
12
12
24

^

m

- t 'A

= t

D . 1005,5s

B. 1005s

C. 2012 s

2T[

Theo bai ra ta c6: v = -167csin(27tt ~ ^ )
= ^ + k2n
6

t=- +k
6

= — + k27t

"^"^

keN

•y

+12

la t h o i gian de vat d i qua v j t r i x = 2cm Ian t h i i 2 ke t u t h o i d i e m ban

d a u u n g v a i k = 0 (nghiem d u a i ) .

Vay

2

^

^ N-2„
^
2012-2,
1
t=
T + t, =
.1 + - = 1005,5 (s)
^

2

2

6

=> ban dau vat 6 M .

Vat qua v j t r i can t i m Ian t h u 2 tai P k h i d o

= ^^^I^T +1

^^Y^T +12

= 1005,5T = 1005,5(s)

A.

-s
8

B.

c. 5s

—s
24

^

'

D . 1,5s

8

'Pkan tich vd hu&ng ddn gidi
Cach 1: G i a i theo p h u a n g trinh lugng giac

I

2^ ^

Vat qua v i t r i x = 2cm Ian t h u 2012 la :

2

- —

1
2*2 2
Wd = W t r ^ - m c o ^ A ^ s i n ^ 2 7 r t - ^ = - m o ) A cos 2nt2
2
3^

t. =i + k = - + 0-i(s)
2

Pha ban dau c =
p

Nhan xet: a day ta hieu dien duang tron theo v detinh nhanh han.
C a u 2: M o t vat dao d o n g dieu hoa v o i p h u a n g t r i n h x = 8cos(27it - —) cm.
3
T h a i d i e m t h u nhat vat qua v i t r i c6 d o n g nang bang the nang.

N-2,
Vat qua Ian t h u 2012 (chan) nen ta d u n g cong thuc : t = — ^ — T
Voi

—

2

t r i vat d i qua la N va P.

t=

t= l . k
2

6

=> V =

Qua Ian t h u 2012:

Cach 1: G i a i theo p h u a n g trinh lugng giac

6

2

vat quay d u o c n u a v o n g nen mat ^2

C h u k y dao d p n g : T = — = — = l(s)

27rt —

-1

T

'Phdn tich ra hu&ng ddn gidi

6

-871

N h i n tren d u a n g t r o n ta thay v j

2012 vat qua v j t r i c6 v = -87t cm/s.

2ni-^

Theo bai ra:
167r

C a u 1: M p t vat dao d o n g dieu hoa vai x = 8cos(27it - —) c m . T h a i d i e m t h i i
6

C
O

Khang Viet

T i n h theo van toe

V

B A I T A P VAN DUNG:

A . 1005,5s

+

DWH

o

sm
1-cos

2nt-^

3

2nt-^

= cos

3

3.

3

1 + cos 4 7 t t -

47tt

n

271^

V a y chpn dap an A
C a c h 2: S u diing d u a n g tron lug^ng giac
+

T i n h theo i i d o
Ta CO X =

A^-

= ±4%/3(c m .

cos

47tt-

2n^

A

.

.

= 0=>47it

7t ,
^
7
k
= — + k7r=:>t = — + — k e [ - l ; « . )

3
2
24
4

27t

T h o i d i e m t h u nhat u n g v o i k = - 1

t = —(s)
24^ '

rf ••^•Ii^,,..•

V i v < 0 nen vat qua M i va M2. Qua Ian t h u 2012

C h u y: vi thai gian khong nhan gia tri am nen thai diem thu nhat ung vai gia tri k

t h i p h a i quay 1005 v o n g roi d i t u Mo den M2.

nho nhat ma lam cho t > 0.

Goc que| A(p = 1005.271 + 71 => t = 1005,5 s .
18

19


Biquyet

on luyftt thi d^i hgc dat diem tot da Vat It, tap 1 - Le Van Vinh

D ? n g 4 . X a c d i n h s o I a n v a t d i q u a x t r o n g thcfi g i a n tu" t i d e n
tz ( A t = t 2 - t i )

Cach 2: S u dung duong tron lugng giac
x=±

Wd = W .

A

72

pHl/aNG PHAP
» Trong mpt chu ky T (27i) vat di qua x 2 Ian neu khong ke den chieu
chuyen dpng, neu ke den chieu chuyen dpng thi se d i qua 1 Ian

• CO 4 v i tri M i , M 2 , M a , M 4 tren duang tron.
Pha ban dau c = — nen ban dau vat a
p

Mo

3

*

.
n

Goc quet: A(p =

n

n
^ A ( p l
= — =>t =
= —s

4

3

12

C
O

Xac dinh M dua vao x (hoac v, a, Wt, W d , F)

*

ling voi vat di t u M o den M 4 .

Xac dinh M i dua vao ti v a PT x,v ( xi, v i chi quan tam < 0 hay > 0 hay = 0)

*

Thoi diem dau tien vat qua v i tri W d = W t

A p dung cong thuc A(p = coAt tim so'Ian

''

Cdc loai thudng gap va cong thuc tinh nhanh
Acp coAt

24

271

,i

= n,p(n + 0,p)

27t

Neu khong ke den chieu: N = 2n + N'
Cau 3:

Mot vat dao dpng dieu hoa voi phuong trinh x = 8cos(7rt - —) cm.

N' la so ian di qua x khi tren vong trong lupng giac quay dupe goc 0,p.27t

4

ke tir vi tri ban dau

Thoi diem thu 2010 vat qua vj tri c6 dong nang bSng 3 Ian thenang.?
Cach 1: giai theo phuong trinh lugng giac

Wd = 3Wt

^ sin

2.t-^ =
2

^

3

2,tt-^ = - ^

TTt-^

4

= 3cos^

>cos

4

k27i

t = —+ k k e N
12

+ k2K

t = - —+ k
12

1
"2

Qua Ian thu 2010 (chin): t =

N-2

Neu ke den chieu: N = n + N '
N' la so Ian di qua x theo chieu bai toan quy dinh khi tren vong trong
lupng giac quay dupe goc 0,p.27t ke t u vj tri ban dau

m vi D U M A U :
V i d u 1: Cho vat dao dpng dieu hoa theo phuong trinh:

keN

T + t, =

X = 3cos

2010-2 „ 11 12059
-.2 + — = .
(s)
12
12

4

A. 4

B. 5

C. 6

D. 7

Cach 1: Giai theo phuong trinh lugfng giac

2

=> CO 4 v i t r i tren duong tron M i , M2, M s , M4.

Vat qua vj tri x = 1,5 cm ta c6:

Qua ian thu 2010 thi phai quay 502 vong

3

cos

47tt--

(moi vong qua 4 Ian) roi di t u M o den M2.
Goc quet

4nt-^

A(p = 502.271 + 71 ^

=1004Tt +
.3

C
O

12

.

12

4)

= > t = ^ = 1004.11 = l ^ s

20

cm.

'Phdn tick vd hu&ng dan gidi

W , = iw=>x = ± '

47rt-^
3,

So Ian vat di qua v i tri x = 1,5cm trong 1,2s dau tien

Cach 2: S u d\ing ducmg tron lugfng giac
Wd = 3Wt

, ,...

12

3

= 1,5 => cos
= ^ + k2n
3

4 n t - i ^ = - ^ + 127r
3

3

t

2
3
1 k
= - + - (keZ)
6 2^
t =

l

(leZ)

Trong 1,2s dau tien tuc:

21


Bi(juyei

on

luyen

0 < t <1,2<=>

thi

itai hoc

itat dicin

0 < i + ii6 2
0<-2

tot da

Vat

li, i,ij> I - Le V&ti

-0,330<1<2,4

Vitth

k = 0;l;2
1 = 0;1;2

Chu y rang: moi gid tri k vd I tuomg ung vai moi Ian vat qua vi tri x = 1,5 cm.
CO 3 gid tri cua kvd3 gid tri cua I nen c6 tat cd 6 Ian vat di qua vi tri x = 1,5 cm
Cach 2: Su d\ing duong tron lugng giac
Pha ban dau (p = - — nen ban dau vat 6 diem B.
3
Ta can xac djnh so'Ian di qua li dp 1,5 ung vai hai diem A, B.
Ta c6: At = 1,2s;

CtyTNHIt

Chttyen de 2

T A N S<5 - C H U

\

/

I

n W H

K h a

- BI£:N £>0

pHl/aNG PHAP
* Chu ki (T): cua dao dpng dieu hoa la khoang thoi gian de vat thuc hi^n
mot dao dpng toan phan. Don vi la s
*

Tan so (fl: cua dao dpng dieu hoa la so dao dpng tuan hoan thyc hi^n
trong mpt s. Don vi la 1/s hoac Hz.

*

T -0,5s => At = 2T + 0,2 => N = 2.2 + N '

Tan so goc

(m);

Giira tan so goc, chu k\a tan so lien he nhau: c = ^
o

= 27rf

Con lac 16 xo la dao dpng dieu hoa th'i:

Bay gia ta tinh N ' .

= J^;

Goi M la v i t r i cua vat tai thoi diem t = 1,2s.
Goc ma vat quet dugc trong 0,2s la:

Tan so goc: «

Tan so: f =

BOM = A(p = co.At = 47t.0,2 = 0, Snrad

He thuc dpc lap giiia li dp va van toe: A'^ = x + - y

2

Ta c6: BOM > AOB => vat di qua A
=^N' = 1 + 1 = 2 ii> N = 2.2 + 2 = 6.
Vay

CO

6 Ian vat di qua vj tri c6 l i dp 1,5 cm

27t^

2
CO

Goc ma v|t quet dupe t u A den B la:

AOB = — r a d .
,
3
So sanh hai gia trj tren

; Chu ki: T =

v^

2

He thuc doc lap giua van toe va gia toe: A = — j - +
CO

CO

Chieu dai quy dao: S = 2A

m vi

DU

MAU:

Vi d u 1: (Trich de thi thu chuyen Nguyen Quang Dieu - Dong Thap Ian
1 nam 2013)
Mpt eon lac 16 xo dao dpng dieu h6a theo phuong n3m ngang c6 khoi
lupng m = lOOg, dp ciing k = lON/m. Keo vat ra khoi vj tri can bang mpt
khoang 2em roi truyen eho vat mpt toe dp 20em/s theo phuong dao
dpng. Bien dp dao dpng cua vat la:

A. 2^/2 cm.

B. V2 cm.

C. 4 cm.

D. 2 cm.

' ' '

^hdn tkh vd hit&ng dan gidi
Vai bdi todn nay chi can tim dugc tan so goc roi thd vao he thuc doc lap la cd ngay
bien do.
Tan so goc: co = . t =
Vm

i ^ . = lOrad / s

V0,1

Theo h ^ thuc dpc lap lien h^ giiia li dp va van toe:

22

9

A 22 = x 2 + 4 = 2 ' + ^
A =X2 +

Chpn dap an A

co^

10^

= 8=^A = 2V2em

23


V l d u 2: (Trich de thi thu Nam T r ^ c - Nam D i n h Ian 1 nam 2013)

todn ve'luc, each gidi chung nhat Id tim hap luc tdc dung vdo vat gay ra gia toe

M p t vat dao d o n g d i e u hoa v o i gia toe cue dai amax va toe d p c^c dai Vmax.
Tan so dao d o n g la
£_

chuyen dong cho vat.
Cach giai bai nay n h u sau:

^max

g

£_

^max

Q f _ ^^-^max

-Q £ _

^max

Con lac dao d p n g tren doan thang dai 4cm chinh la q u y dao chuyen d p n g
ciia vat S = 2 A = 4 c m , v i the bien dp dao d o n g cua vat la A = 2cm.
K h i vat m dao dong, h o p luc cua luc d i ? n t r u o n g va luc dan h o i gay gia toe

^ h d n (icfi pd huang ddn gidi

a cho vat.
Bdi nay dan gidn chi Id tim moi lien he giua gia toe cue dai vd toe do cue dai.

Tai v i t r i bien, vat c6 gia toe cue dai. K h i do ta c6: Fd - Fdh = m.amax

Gia toe cue dai: a^^^ = co^A
qE - k A =
Toe dQ cue dai: v^^^

T u day ta lap t i le la eo ngay lien
a„.^^

o^A
(oA

e6n phia d u a l gan vat m . N a n g m len den v j t r i 16 xo k h o n g bien d a n g roi
tha nhe vat dao d o n g dieu h6a theo p h u o n g thang d u n g v a i bien do

V l d u 3 : (Trich de thi thu Nghi Lgc 4 - Ngh? A n Ian 1 nam 2013)

2,5cm. L a y g = lOm/s^. T r o n g qua t r i n h dao dong, t r o n g luc ciia m eo eong

M o t vat dao d o n g d i e u hoa tren quy dao dai 40em. K h i d o d a i la 10cm
vat CO van toe 2071V3 cm/s. Lay TC^ = 10. C h u k i dao d o n g cua vat la:

^hdn

C. 0,5s

A . 0,41W

C. 0,5W

D . 0,32W

ddn gidi

Day Cling la dang todn doc vdo rat la, tuy nhien degidi quyel bdi todn ndy cdc ban chi
can nha vecong thiec tinh eong suat ciia luc md da hoc tie cdc lap dual. P^^ = F.v
Vai F Id luc tdc dung vdo vat, v Id van toe chuyen dong ciia vat.

K h i do d a i vat la lOcm nen l i dp x = ± 1 0 c m

Trong dao dong dieu hoa, van toe chuyen dong cua vat Id van toe tiec thai nen eong

De cho q u y dao dai S = 2 A = 40 ^ A = 20cm

suat ciia luc cung Id eong suat tiec thai.

A p d u n g he thuc doc lap lien he giira l i do va van toe

Sau day la each giai cu the bai toan nay:

207t73
- = 1=>C0 = -

(coAf

B. 0,64W

tich vd hu&ng ddn gidi

bien do niea Id dii.

A'

suat tuc t h o i cue dai bang

D.5s

Bdi todn ttm chu ky (tan so) tie he thiec doc lap, decho li do, van toe vi the can tim

•+

qE = 2 k A =i> E = 2.10^ V / m

V l d u 5 : M 6 t eon lac 16 xo c6 do c u n g k = 4 0 N / m dau tren d u p e giir eo d j n h

271 v „ 3 ^

B. I s

A = m. — .A »
m

Chgri dap an A

giiia hai dai l u o n g tren

„ ,
,
l a
= (0 = 27rf =^ f = _ : i ! B a x . . c h p n dap an A

A . 0,1s

m.w2

= coA

Cong suat tuc t h 6 i cua t r p n g luc P „ = P.v = m g v v o i v la van toe cua vat m .
= 27trad/s=>T = —= — = l s

VA2-X2

720^-10^

«

fir

271

V o i m va g la cae hang so nen P^sUax '^'^n\ax=

C h p n dap an B
V l d u 4 : M o t con lac 16 xo n a m ngang g o m vat nang tich d i f n q = 20|LIC va

PcsMax = mgVmax = ^ g A

16 xo CO do c u n g k = l O N / m . K h i vat dang n a m can bang, each d i ^ n , tren

— = g A ^ / k ^ (1)

=

J—A
Vm

Vm

mat ban nhan t h i xua't hien tuc t h o i m o t d i f n t r u a n g deu t r o n g k h o n g

Theo bai ra: nang m len den v j t r i 16 xo k h o n g bien d a n g r o i tha nh? nen

gian bao q u a n h c6 h u a n g dpe theo true 16 xo. Sau do eon lac dao d o n g

bien dp dao d p n g A = Al

tren m o t doan thang dai 4cm. D o Ion c u a n g d g d i ^ n t r u a n g E la:

^, m g
kA
D p bien d a n g cua 16 xo tai VTCB: Al = — = A = > m - —

A . 2.10^ V / m .

B. 2,5.10^ V / m .
^hdn

Thong thuang

C . 1,5.10^ V / m .

ir„ •;
..W ? j ; ,

D.lO^V/m.

tich vd huang ddn gidi

thi bdi todn eo liec la tdc dung vdo vat trong qud trlnh dao dong

Thay vao (1):
PcsMax = g A V k i ^ = ^^f'Y

^

^ 40.2,5.10-2 VlO.2,5.10-2 ^

thuang dugc xet vai con Idc dan. Tuy nhien a day bdi todn xet cho con lie Id xo nen
nhieu ban se xem day Id dang todn la vd thuang bo qua. Nhin chung thi cdc bdi
24

C h p n dap an C
25


Bi quyei on luy$n thi deii hqc dat diem tot da Vat li, tap 1-Le

Van Vinh

Fmax

V i dM 6 : (Trich de thi thu Quynh L i n i 1 - Ngh# An Ian 1 nam 2013)
Treo con \ic 16 xo tren tran cua mpt thang may, khi thang may dung yen thi chu
ky cua con lac la T, cho thang may chuyen dgng di xuong nhanh dan deu voi
gia toe a = 0,5g (g la gia toe roi ty do) theo phuong thang dung thi chu ky dao
dong dieu hoa cua no la T' va
A.T' =

2T.

B . T ' = T.

= 0,5T.

C.T'

D.T' = T V 2 .

^han tick Pd huang ddn gidi

A + Al

=^

76

= -

k
^

75

75

,„..

Chpn dap an B
Nhan xet: khi tim ra Al = 2,25(m) nhieu ban se boi roi vi qua Ion so vai cac dap
an decho. Cac ban nen binh tinh khai thdc gid thiet ticp theo ma tinh cho ra ddp so
Ndi chung Id hay binh tinh!

g' = g - a = g - 0 , 5 g = 0,5g

Al

Chu ky con lac thang may diing yen: T = 2n^ j—
=

(A + Al)

=^

sau do so sdnh vai ddp an. NeU c6 thi minh da diing con nen sai thi hay xem Iqi.

Xuong v i nhanh dan deu a i vi the F^, T nguoc voi P i suy ra

Chu ky con lac thang may chuyen dpng: T' = 2n^j^ = 2n / ^

k ( A + Al)

T h e o b a i r a : - ^ = -4^

V2T

V i the chpn dap an D

Ca B A I TAP V A N DUNG:
Cau 1 : (Trich de thi thu chuyen Hong Linh Ha tinh Ian 1 nam 2013)
Con 15c 16 xo c6 dp cung k va vat nho khoi lupng m c6 the dao dpng khong
ma sat tren mat phSng nghieng goe a so voi phuong ngang. 6 vi tri can
bang dp bien dang cua 16 xo la Al. Cho gia toe roi t u do tai do la g thi chu ky
dao dpng la

A.T = 2.pL:.

B.T = 2 . I ^ .

Ral tiec r^ng day khong phdi la dap an dung ma deym cau, vqy chung ta da sat lam tit
dau?. Rieng chu ky con lac Id xo thi chi phu thuoc vao dp cimg cua Id xo va khoi luang
am vat nqng ma khong phu thuoc vao vi tri dqt con lac nen khong phu thuoc vao gia toe C.T = 27:
D . T = 27i
trpng tru'ong. KJji thang may chuyen dong thi gia toe trpng tnecmg cua con lac sS la gia
^gsina
VAl
toe trong tntang hicu dung thay doi nhimg chu ki/ khong phu thuoc vao gia toe trong
tnfcmg nen chu ky con idc vi the'ding khong doi. Dap an B m&i la dap an dung.
Chu ky eon 15c 16 xo dao dpng dieu hoa tren mat p h i n g nghieng goe a so
ChgnB
voi phuong ngang: T = 27t J— = 2n
k
ygsina
Vi d u 7: (Trich de thi thu Quynh Lini 1 - Nghf An Ian 1 nam 2013)
Mot con lie 16 xo treo thSng diing dupe kich thich eho dao dpng dieu hoa.
Th6i gian qua cau di tir vj tri cao nhat deh vj tri thap nhat la 1,5s va ti so'giua
dp Ion cua lire dan hoi 16 xo va trpng lupng qua cau gan a dau con lac khi no 6
vj tri thap nha't la 76/75. Lay g = v} (m/s^). Bien dp dao dpng cua con lac la:
A. 4cm.
B.3cm.
C2cm
D.5cm.
'Phan tich v>d huang dan gidi
Thoi gian qua cau di tu vj tri cao nhat den vj tri thap nhat ehinh la di tu bien nay
qua bien kia mat — = 1,5 => T = 3(s).
Dp bien dang 16 xo tai VTCB: T = 27i

Vi the chpn C
Cau 2: (Trich de thi thu Nguyen Dinh Chieu - Tien Giang Ian 1 nam 2013)
Mpt con lac 16 xo, gom 16 xo nh^ c6 dp cung 50N/m, vat c6 khoi lupng 2kg,
dao dpng dieu hoa doc. Tai thoi diem vat co gia toe 75 cm/s^ thi no co van
toe 15^y3 (cm/s). Xac djnh bien dp.
A.A=6cm.

B. A=9em.

g

47t^

10.32

40

= 2,25(m)

D. A=10em.

(phdn tich ra huang ddn gidi
Tan so goe: (o =

gT^ _

C. A=5em.

=

= 5 rad / s

thiic dpc lap lien h^ giua van toe va gia toe:
v^

a'

'

a'

^

Luc dan hoi 6 vj tri thap nhat la lire dan hoi cue dai: F^g^ = k ( A + Al)
27
26


'Phdn tich v>d huang dan gidi
=> A =

= 6cm

20
= 10rad/s
0,2
He thuc dpc lap lien h? giiia van toe va gia toe:
Tan so goc: c = ^j— =
o

Chgn dap an A
Cau

2: (Chuyen Ha Tinh Ian 1 nam 2013)

(I) dieu ki^n kich thich ban dau de con lac dao dpng; (II) chieu dai day treo;
Chu ky dao dong nho ciia con lac dan phu thupc vao:
A. (II) va (IV).

B. (Ill) va (IV).

C. (II) va (V).

D. (I).

^hdn tkh v>d hu&ng dan gidi
Ta bie't rang: chu ky con lac dan dao dong dieu hoa phu thupc vao chieu dai
day treo va gia toe trong truong. Chpn dap an C
Cau 3: (Trich de thi thu chuyen Tran Phu Thanh Hoa Ian 1 nam 2013)
Mot con lac 16 xo thang dung 6 vj tri can bang 16 xo gian mot doan A/ . Neu
chieu dai 16 xo dupe cat ngan chi c6n bang 1/4 chieu dai ban dau thi chu ki
dao dpng ciia con lac 16 xo bay gi6 la

=

—+ •

(III) bien dp dao dong; (IV) khoi lugng vat nang; (V) gia toe trong truong,

•A=

10

v2
- ^

+

I (0

— 7 -

CO

co^A^

= 1

(200V3)

20^

10^

10^

= 4cm

:<• t o r

''

Chpn dap an D
Cau 5: (Trich de thi thii chuyen Ha Long Quang Tri Ian 1 nam 2013)
Con lie 16 xo CO khoi lupng vat nang la 85g dao dpng dieu hoa, trong 24s
thuc hi^n dupe 120 dao dpng toan phan. Lay

= 10. Dp cung ciia 16 xo ciia

con lac do la

y j

A. 85N/m.

B. lOON/m.

C. 120N/m.

D. l O N / m .

^hdn tich v>d huang dan gidi
Chu ky con lac 16 xo :
^

/m

At

4n^n^.m

k

^

^hdn tick m hu&ng dan gidi

n

At^

Gpi k va k' la dp cung ung voi 16 xo c6 chieu dai / va 1/4.
Dp cung va chieu dai 16 xo lien h^ qua cong thuc: kl = k'—=> k' = Ak
4
Dp gian ciia con lac 16 xo c6 chieu dai / tai VTCB:
- P ô k A l = mg=>-^ =
k
g

47t^l20^.0,085
ã = 85N/m
24^

Chpn dap an A
Cau

6 (Trich de t h i dgii hpc nam 2013): Mot con lac 16 xo c6 khoi lupng vat

nho la m j = 300g dao dpng dieu h6a voi chu ki Is. Neu thay vat nho c6
khoi lupng mi bang vat nho co khoi lupng m2 thi con lac dao dpng voi chu

ki 0,5s. Gia tri m2 bang
A. lOOg

B. 150g

C.25g

D. 75 g

^hdn tich vd hu&ng dan gidi
Chu ky con lac 16 xo voi chieu dai //4:

Chu ky dao dpng cua con lac co khoi lupng mi va mi Ian lupt la:
Tj = 2n

Chpn dap an A
Cau 4: (Trich de thi thu chuyen Nhu Thanh Thanh Hoa Ian 1 nam 2013)
Mot con lac 16 xo c6 dp cung k = 20N/m, khoi lupng m = 0,2kg dao dpng
dieu h6a. Tai th6i diem t, van toe va gia toe eua vien bi Ian lupt la 20 cm/s va
2V3 m/s^. Bien dp dao dpng ciia vat nang la:
A. l O V S c m .
B. 16 cm.
C. 4 V 3 e m .
28

D. 4 cm.

mj _ Tj

2

m2 = nij.

1

[^2 J

= 300.

ro,5^

11J

= 75g

Chpn dap an D
CSu 7: (Chuyen Diic Thp Ha Tinh Ian 1 nam 2013)
Hai chat diem dao dpng dieu hoa dpc theo hai duang thang song song vai
tryc Ox, canh nhau, cung bien dp va tan so. V i tri can bang ciia chiing xem
29


n h u t r i i n g nhau (cung toa do). Biet rSng k h i d i ngang qua nhau, hai cha't d i e m
chuyen d o n g ngugc chieu nhau va deu c6 dp Ian l i do bang m p t nua bien dp.
H i e u pha cua hai dao d p n g nay c6 the la gia trj nao sau day:
C. 7i;

3

D.

271

^hdn tich ra hudrng ddn gidi

Theobaira:

=l i n . ^

=^

= 48cm

Dp bien dang ciia 16 xo tai VTCB:
1

(K^A\ — 1 ^ =
Al
4n^r

= 0,012m = 1,2cm
40.4,5^

. i^r;; v,';

Vay: IQ = l^b - ^1 = 48 - 1 , 2 = 46,8cm

V i hai vat dao d o n g dieu hoa ciing

•

,•

Chpn dap an D

bien d p va tan so nen ta bleu dien tren

cau

m o t v o n g tron n h u h i n h ve.

10: (Trich de thi thu chuyen Phiic Trach H a T i n h Ian 2 nam 2013)

Mot con lac 16 xo c6 k= lOON/m, dau tren co dinh c6n dau d u o i gan vat nang

H i e u pha ciia hai dao d p n g tren la — .
3
C h p n dap an D

i n = 0,4kg. Cho vat nang m dao dpng dieu h6a theo p h u o n g thang d i m g thi thay
thai gian 16 xo nen trong mpt chu k i la 0,1s. Cho g= 10 m/s^ «

m/s\n dp dao

dpng ciia vat la
Cau

A.8>/3cm

8: (Chuyen D u e T h p H a T i n h Ian 1 nam 2013)

B.4cm

DA^cm

'Phdn tich vd hu&ng ddn gidi

M o t vat CO k h o i l u p n g m = lOOg d u p e tich dien tich q = - l O ^ C gSn vao 16 xo
CO dp c u n g k = 40N/m dat tren mat phang ngang k h o n g ma sat. Ban dau

C. 4^2 cm

L 6 xo nen

khi

A l < A . T h a i gian 16 xo nen k h i vat dao

d p n g tir

n g u a i ta thie't lap m o t dien t r u o n g nSm ngang, c6 h u a n g t r i i n g v a i true cua

- A l - > - A - > - A l (chieu d u a n g chpn thSng d u n g h u o n g x u o n g ) . V i the 16 xo

16 xo, CO c u o n g dp E = 8.10^V/m, k h i do vat d u n g yen 6 v j t r i can bang.

nen t r o n g m p t chu ky gap hai Ian t h o i gian vat d i tir - A l - > - A .

N g u o i ta d p t ngpt ngat dien t r u o n g . Sau k h i ngat dien t r u o n g vat dao d p n g

tn = 2 t ( _ ^ _ _ A ) = 0,1 => t ( _ ^ , ^ _ A ) = 0 , 0 5 ( 5 )

dieu hoa v o i bien dp bang
A . 12,5cm.

B. 2,5cm;

C. 4cm;

D . 2cm;

Goc vat qu^t d u p e t r o n g thai gian tren:

'Phdn tich m huang ddn gidi

cp = « . t ( _ „ _ A )

K h i CO dJQn t r u o n g vat d i r n g yen 6 v i t r i can bSng, k h i d o luc d i e n t r u o n g
can bang v o i luc dan hoi (phuc hoi). K h i d o t ngpt ngSt d i e n t r u o n g , vat se
bat dau dco d p n g dieu h6a v o i vj t r i bien dp la v j t r i vat can bang cu. Luc
cfo:

Fdt = F d h M a x «>

q E = k A =^ A =

qlE
k

-10

-6

.8.10^

40

= 0,02m = 2cm

C h p n dap an D
Cau

-Al
coscp =
-A

Al
= — =>A
A

^

.0,05

Al

mg
=

=
cos

-rad

0,4.10

— =
kcoscp

4^2
=

V2

. r^r
m = 4v2em

100

•2
11: (Trich de thi thu chuyen T h i | u Hoa T h a n h Hoa Ian 2 nam 2013)

Con lac 16 xo dat tren mat phSng nghieng goc a k h o n g ma sat t h i chu k i dao

M o t con lac 16 xo trco thang diirng va dao d p n g d i e u hoa v o i tan so'

d p n g rieng ciia con lac p h u thupc vao

f = 4,5Hz. T r o n g qua t r i n h dao d p n g chieu dai ciia 16 xo bien thien tir 40cm

A . goc a va dp cirng 16 xo.

den 56cm. Lay g = lOm/s^. Chieu dai t u nhien ciia 16 xo la:

B. goc a, k h o l l u p n g vat va d p c u n g 16 xo.

A . 48 cm

B. 42 cm

C. 40 c m

D . 46,8 c m

'Phdn tich m hudrng ddn gidi
Ta biet r^ng: Chieu dai t u nhien ciia 16 xo treo thang d u n g tinh theo cong thuc;
'() ~ 'cb ~ ^ ' v i the'ta can t i m chieu dai cua 16 xo tai VTCB va dp gian ciia 16 xo tai
\TCB.
30

=

C h p n dap an C
Cau

9: (Trich de thi thtr chuyen V I n h Phuc Ian 1 nam 2013)

=^-.t(_^,_A)

1. kho'i l u p n g cua vat va dp c u n g 16 xo.
). goc a va kho'i l u p n g ciia vat.

*'

*ã

<

ã ô

''

'

^hdn tich vd hu&ng ddn gidi
Ihxi k y con lac 16 xo dao d p n g dieu h6a tren mat p h a n g nghieng goc a so
Al
/oi p h u o n g ngang: T = 27i./— = In
Vk
\ gsina
31


Cty TNHH

m llUya M lUy^U tht dul /.<.. ,h,t diem tot da Viit It, tap 1 - Le Van Vitth

Nhin vao cong thiic nhieu ban ket luan rang: chu ky dao dong rieng cua con
idc Id xo dat nim nghieng ngoai phu thuoc vao do ci'tng va khoi luang ma con phu
thuoc vao goc a,

gia toe g va do bien dang cua Id xo tai VTCB AI. Chac c6 le so

litong kel luqn dieu nay se khong it dung khong cdc ban! Tuy nhien kei luan the
nay la sai ban chat nghiem trong day. Theo nhu dinh nghia ve chu ky dao dong
rieng cua con idc id xo dao dong dieu hda thi: chu ky cua dao dong rieng chi phu
thuoc vao dac tinh cua he ma & day la do ci'mg cua Id xo va khoi luang cua vat
nqng. Cdc ban phdi bam sdt vao dinh nghia ma chon dap dn cho chinh xdc nhe! Dap
an cudi cimg Id C vi Id xo cd dat trong tu the ndo thi chu ky cua no van chi phu
thuoc vao do cimg cua Id xo va khoi Iwgng cua vat nqng thoi.

Chpn dap an C
C a u 1 2 : (Trich de thi thu chuyen Nguyen Thi Minh Khai - Ha tinh Ian 1
nam 2013)
Mot con lac 16 xo treo thang dung trong thang may. Khi thang may di len

MTV

Viet


1
-1
Bien dp dao dpng con lac A = "^'^ ^
Dp bien dang 6 VTCB: ^1 = ^

=

=

48-32

= 8cm

= O'^^m = 16cm

Chieu dai ban dau
lmax=lo+Al + A ^ l o = l ^

A - A l = 4 8 - 8 - 1 6 = 24cm

Tai thai diem ma vat a v i tri tha'p nhat thi cho thang may d i xuo'ng nhanh
dan deu voi gia toe a = - j ^ liic do eon lie chju tac dung luc quan tinh
= ma = 0,4.1 = 0,4N huong len. (xuo'ng v i nhanh dan deu a 4'^ Fqt t )
Lyc nay se gay ra bien dang them cho vat doan:
X=^

nhanh dan deu voi gia toe a = g / 4 thi tai vi tri can bang 16 xo bj dan doan

k

= M = 0,016m = l,6em
25

,fi, ;

12,5cm. Chu ki dao dong rieng ciia con lac 16 xo la

Vay sau do vat dao dpng bien d p : A ' = A + x = 8 + l,6 = 9,6cm

A. |(s).

Chpn dap an D

B. 7t(s.)

C.2(s).

C a u 1 4 : Mot eon lac 16 xo dang can bang tren mat phSng nghieng mpt goc

'Phdn tich cd hit&ng dan giai
Thang may di len : v t nhanh dan deu nen a t v i the luc quan tinh ^

i

cung chieu voi P.

Fq, i+Pi

+Fdh t= d <=> ma + mg - kAlg = 0<::>m^ + m g - kAlo = 0

o^-kAlo=0=>Ji =A
4

m

4Alo

=^

4.0,125

VlOO

dai them 2cm. Bo qua ma sat, lay g « 1 0 m / s ^ ; sin 37" * 0,6. Tan so goc dao

<Phdn tich v>d huong dan gidi
Dp gian cua 16 xo tai VTCB doi voi eon lac 16 xo dat nghieng mpt goc 37" so

A l o 2 = - ^ s i n ( a + Aa)

k

C a u 1 3 : Trong thang may treo mpt con lac 16 xo c6 do cung 25N/m, vat nang
CO khoi lugng 400 g. Khi thang may dung yen ta cho con IMc dao dong dieu
hoa, chieu dai con lac thay doi tu 32cm den 48cm. Tai thai diem ma vat 6 vj
tri tha'p nhat thi cho thang may di xuo'ng nhanh dan deu voi gia toe ^ = ^ •
Lay g = TC" = 10 m/s^. Bien dp dao dong ciia vat trong tru6ng hop nay la
B. 19,2 cm.

D. 5(rad/s).

"

.

Khi tang them goc nghieng 16° thi dp gian mai tai VTCB la:

5

Chpn dap an A

A. 17 cm.

C. 15(rad/s).

voi phuong ngang.
1 *i
•
A i mgsina
kAloi = m g s m a = > Aloi =
j^^

= 100

. =^T = 2 . / ^ = 2 . / l L = I s
Vk

37'' so voi phuong ngang. Tang goc nghieng them 16° thi khi can bang 16 xo
dpng rieng cua con lac la:
A. 12,5(rad/s)
B. 10(rad/s).

Cac lire tac dung vao vat tai vj tri can bang:

32

D W H Khang

C. 8,5 cm.

D. 9,6 cm.

(2)

Tu(l) va (2) taco: Aln^ -Aloi = — r s i n ( a + Aa) - sina
k
k grsin(a + Aa)-sina]
lo(sin(37°+16°)-sin37°)
m

AI02-AI0]

0,02

aoo=co^

"(0 = J — =10rad/s . Chpn dap an B
m
33


Bt iiuifet on liiin'ii thi diii hoc 4at diem tot da Vat li, tap 1 - Li Van

Vinh

C a c h 1: T a c h At t h e o T

Chuydn de 3
QUANG BUdNG -

-

TdCfiOTRUNG BINH - V^N TdC TRUNG BINH

Phan tich thanh: At = nT + 0, pT

CAC DANG TOAN VE QUANG Dl/QNG

Ve duang tron lugng giac, suy ra quang duang vat di duoc la S = Si + S2

D ^ n g 1 . Q u a n g d U d n g v a t d i dUcrc uTng v d i k h o a n g t h d i g i a n
dac b i ^ t
+ Quang duong di trong 1 chu ky luon la 4A; trong 1/2 chu ky luon la 2A
+ Quang duong di trong 1/4 chu ky khi vat di t u VTCB den vi tri bien hoac
ngugc lai la A.

m \li DU
VI

+ Trong do Si la quang duang vat d i duoc trong n.T (chu ky) hay
Si = n.4A va S2 la quang duong vat di dugc trong thoi gian 0,pT .
De xac dinh S2 ta xac dinh goc quet cp tren vong tron (p = co.O, pT t u do suy
ra S2.
T

MAU:

C a c h 2: T a c h At t h e o

du 1 :
Mot vat dao dpng dieu hoa theo phuong trinh x = 4cos

3

-

(cm).

Tinh quang duong ma vat di duoc trong thai gian 3,5(s)?
A. 39cm

L a p t y s o Y = r>,p = n + 0,p v 6 i n = 0 ; l ; 2

B. 15cm

C. 56cm

-

D. 32cm

^han tick m huang dan gidi
Bai todn khong cho thai diem ban dau ti vat d dau, vi theneu ti le thai gian khong

lap ti so: ^ = n,p-

-

n + 0,pvoi n = 0; 1; 2

T
T
Phan tich thanh: At = n — + 0,p—
2
^2
Vay quang duang vat di la S = S ; + S2 = n.2A + S2

ndm trong truang hap dac Met thi bdi todn se di vdo be tat. Do do ta can xdc dinh ti

T
S2 la quang duong vat di dugc trong thoi gian 0, p — ke t u v i t r i xi, v i .

sotren c6 gid tri nguyen hoac bdn nguyen hay khong.

De xac dinh S2 ta dung vong tron lugng giac (goc quay t u v i t r i ban dau

Chu ky dao dpng cua vat: T = Is

T

Ta lap ti so giua khoang thoi gian de cho vai chu ky dao dong ciia vat:
t
3 5
- = ^ = 3,5 (so ban nguyen)

(p = (o.0,p— = 0,p.7r)
C a c h 3: T i m n g a y g o c q u a y ,

Tu do ta phan tich: t = 3T + 0,5T

+ voi thai gian ti = 3T =>

— =
71

= 3.4A = 12A = 48(cm);
-

+ voi thoi gian t2 = 0,5T ^ 8 2 = 0,5.4A = 2A = 8(cm)

-

S = Si + S2 = 48 + 8 = 56(cm). C h p n d a p a n C

-

khi quay goc A(p = 7r.0,p t u v i tri ban dau (xi, vi) ta dua vao vong trgn
vay quang duang vat d i dugc la S = S j + S2 = n.2A + S2

DU MAU:
V I d u 2 : (Trich dethi thtt chuyen Trdn Phu - Thanh Hoa Idn 1 nam 2013):
Mgt con 13c 16 xo gom mgt vat nang m = lOOg mac voi 16 xo c6 dg cung

Cach lam:

34

se quay goc nn + 0,pn)
khi quay goc nn vat d i duoc quang duang S j = n.2A
lugng giac ta tim dugc quang duang di la $2

D a n g 2 . Q u a n g d i T d n g v a t d i du'^c tCr t h d i d i e m t i d e n t 2 .
At = t 2 - t i
Tu duy loai nay: trong thai gian T/2 (goc quay tren vdng trbn la: n) vat dddh
se di duoc quang duang la lA. Ta de xdc dinh quang duong di duoc neu thai
gian Id nho han T/2 (goc quay nho han n) dua vdo vdng tron luong gidc
Buac bat huge: tim vi tri ban dau: t = ti tim xi vd vi (chi quan tarn > 0, < 0
hay = 0)

= n, p = n + 0, p (nhu vay de d i het thoi gian At tren vong tron
TC

k = 160(N/m) dao dgng dieu h6a giiia hai v i tri bien B va B' quanh VTCB
.

O (cho BB' = I6V2 (cm)). Tinh quang duang v^t d i chuyen dugc sau
35


t/uygr on m y f »

n y t uui mei;i t u i uu vnt

unam

n, lup

i "

CtyTNHHM

L K V M H VTW/I"

khoang thai gian At = — ( s ) , ne'u chpn goc thai gian t = 0 luc v^t d i qua
6,4
B. 151,6 cm
C. 66 cm
'PhcLn tick vd hu&ng dan gidi
2

Theo bai ra: t = 0 liic vat di qua VTCB theo chieu duong chinh la diem Mo
Tan so goc:
™

, ,

„

=,/— =
271

Chu ky: T = —

27t

C
O

= 40 rad / s

6,4

20

Tu hinh ve ta thay S 2 = OA = A.cos^ = 8(cm).
Vay S = Si + S2 = 143,8(cm). Chpn dap an A

Dang 3. Toe dg t r u n g binh cua v a t d i tiT t l i d i d i e m t i den t2:

Tie do ta phan tich: t = 3T + 0,125T

+

Vai thai gian t2 = 0,125T

t2-ti

Vai thoi gian ti = 3T :=> Sj = 3.4A = 96V2(cm);
cp = t j .co = 0,125T. — = - ( r a d ) tir hinh ve ta thay
T
4

S2 = O A = A . c o s - = 8(cm).
4
VayS = S i + 5 2 = 143,8 (cm)
Cach 2: Tach At theo

2
Ta lap ti so giira khoang thoi gian de cho vai nua chu ky dao dpng cua vat:
7t

T
T
At = 6 - + 0 , 2 5 2
2

2
2.20
Vgy quang duang vat di la S = Sj +

m V I DU MAU:
Vi du 3: Mot vat dao dpng dieu hoa theo phuong trinh x = 6cos

A. 16,9cm/s

B. 15,7cm/s

C. 20cm/s

xo, vo.(vi tri vat qua VTCB theo chieu duong)

(cm).
cm

D. 13,2cm/s

Nhan xet: x = -3^/3 = - 6 . — = - A . ^ va x = -3 = -6.1 = - 2
2
2
2

Asll

2

A

^

2

2

0
r

:

S 2 la quang duong vat di dupe trong khoang thoi gian 0,25y ke t u v i tri

^

'Phdn tich vd hic&ng dan gidi

A

= n.2A + 8 2 = 6.2A + S 2

7rt +

4

Trong khoang thai gian ngan nhat khi vat di t u vi tri c6 li dp x = -3
den vi t r i x =3cm, chat diem c6 toe dp trung binh la

A^f3

T

36

vdi S la quang dUdng t i n h nhu" t r e n .

vtbl = -

+

71

'i

VTCB theo chieu duong)

20

1

A(p = 67t + 0,25.7i

S2 la quang duong vat quay dupe 0,25.7t ke t u v} tri xo, vo.(vi t r i vgt qua

= 3,125

4^ = - ^ = 6,25 = 6 + 0,25

^6,25 = 6 + 0,25 ^

n
n
n
Vay quang duong vat di la S = S j + S2 = 6.2A + S2

Ta lap ti so' giiia khoang thoi gian de
cho voi chu ky dao dpng cua vat:
t

Tu hinh ve ta thay S 2 = OA = A.cos = 8(cm).
4
;ã ãã* :;,
ô ã ãằã
'
Vay S = Si + S2 = 143,8(cm)
Cach 3: tim ngay goc quay
Ta lap ti so'giiia goc quay dupe trong khoang thoi gian de cho voi 7t:
40.^'^
A(p^o)At^__M

71

= — = —s

40

Cach 1: Tach At theo T
^

Goc quay ma vat quay dupe trong khoang thoi gian 0,25 —:

D. 132,5 cm

Bien do dao dgng: A = - ^ 5 - = 1^2^^ _ g ^ ^ m
2

K / . , n i v V'irf

cp = co.O,25l = ^ . 0 , 2 5 l = J r a d

VTCB theo chieu duong.
A. 143,8 cm

I V nvVJI

;

'

:
.

^

8
—

T

2

A-JIAS
2
2 ^ _

•]

;
37


Btquyei dn luyfti thi d^i hqc dat diem tot da Vgt It, tap 1-Le

Van Vitth

\f3

Thai gian ngan nhat vat di t u vj tri x = " A . . — den v i tri
AN/3

A
= t Ax/3
2
( - 2 .0)

Lty

A

Thoi gian tu P den Q: t = t

S=

A

2

T

2

1 ^

6

12

12

12

6

MUTlg^Ytcr

>o

1 ^ *| 0 ^ f ) ~ 12^ 12 ~ 6 " 12^
-

Chpn dap an D

JV^-1)A^(V3_1)6^3^^_^^

^2^

'^^i^S.

Toe dp trung binh trong khoang thoi gian tren la:

'tb

V L>VVfl

s
8
V l y van toe trung binh can tim: Vyg = - = ^ = 96 cm / s

T

= t|.

I2^'2 J

Quang duong tuong ung trong thoi gian tren la:
AV3

Ml

= - y la:

T
(-y-»0)

INHH

Bai toan tinh quang dUdng I6n nhat va nho nhat vat
di du'^c trong khoang thdi gian 0 < At < T / 2 .

= - = ^ ^ ^ - ^ = 18(N/3 -1) = 13,2 cm / s

Chpn dap an D

Dang 4 . Van toe trung binh cua vat vt^

mvi

_ | X 2 - X i

t,

- t 1

DU MAU:

V i du 4: Chon cdu trd lai dung

Hinh 1

Mpt vat dao dong dieu hoa tren mot doan thang M N voi phuong trinh:
X = Scos

3.

Vgt CO van toe Ion nha't khi qua VTCB, nho nha't khi qua v i tri bien nen

cm. Gpi O la trung diem cua M N ; P, Q Ian lugt la trung

trong cung mot khoang thoi gian quang duong di dupe cang Ion khi vat

diem cua doan O M va O N . Van toe trung binh ciia vat tren quang duong
tu P den Q la:
A. 16cm/s

B. 32cm/s

C. 64 cm/s

6 cang gan VTCB va cang nho khi cang gan vj tri bien.
Su dung moi lien he giOa dao dpng dieu hoa va chuyen dpng tron deu.

D. 96cm/s

Goc quet Acp = (oAt.

'Pkdn tick pd hu&ng dan gidi

Quang duong Ion nha't khi vat di t u Mi den M2 doi xiing qua true sin

Theo bai ra, ta c6: P la trung diem ciia O M va Q la trung diem cua ON,
-A

» . . Acp ^ . . coAt
Smax = 2 A s m — = 2Asm —
Quang duong nho nha't khi vat di t u Mi den M2 doi xung qua true cos
(
coAt^l
S„i„ = 2 A 1 - cos — = 2A 1 - cos
V
I
2 J
2 )

O

L
12

T

L

-

12

OM

2

A
ON _ _ A
=y''Q=""2
2

Quang duong vat di dug-c: S = |xp - X Q

Luu y: Trong truang hpp At > T/2
T
»
T
Tach At = n —+ At' trong do n e N * ; 0 < At' < —

S =A
Xp =

Hinh 2

2.

+

T
Trong thoi gian n y quang duong luon la 2nA
Trong thoi gian At' thi quang duong Ion nha't (nho nhat) tinh nh^ftren.

= A = 8cm
"' '

39


m JjUyH AH Itliffti tht dat

Hp?

t.n ,la Vat It, iapi-Le

,Ii:„,

V3n

Vinfr

AS_A42_ _A

S „ a ^ = n 2 A + 2 A s i n ^ = n2A + 2 A s i n ^
Smin

+

-A "T~

Acp'
'
coAt'^
= n 2 A + 2A
= n2A + 2A 1 - cos

1 - cos—^
V
—
y

9

2
T

8

I

A
2

Ayfl

A^

8

Toe CJQ trung binh Ion nhat va nho nhat ciia trong khoang thai gian At:

s

s'mir

v a v,bmin = - fAt

^

vtbmax = - 7At^
7

voi Sm.x;

Smin

S

tinh nhu tren.

m

V i DU M A U :
V i d u 5: Mot vat dao dong dieu hoa voi bien dp A va chu ky la T. Tim
quang duong:

T
a. Nho nhat ma vat di dupe trong — .
6
b. Lan nha't ma vat di dupe trong — .
4
2T
c. Nho nhat ma vat di dugc trong
.
^hdn tick v>d huong ddn gidi

Quang duang ma vat di dupe trong — luon la 2A.

2T
Quang duong nho nhat ma vat di dupe trong — chinh la quang duang
3
T
nho nhat ma vat di dupe trong —.
6
T
A(2-N/3).
Theo eau a ta tim dupe quang duong nho nhat ma vat di dupe trong — la
6
2T
Vay quangi
Vay quang duang nho nha't ma vat di dupe trong — la:
3
S ^ i „ = 2 A + A ( 2 - V 3 ) = A(4-V3)

a. Goe ma vat quet dupe trong thoi gian — la: A(p = co.At = — — = 6
T 6 3
Ap dung cong thuc tinh S min t 3 CO'.
l-cos^

2T T
T T
c. D o A t = — > - = > A t = - + 3
2
2 6

=2A 1 - cos— = A ( 2 - V 3 )
6

Vi du 6: (Trich de thi tuyen sinh dai hpc cao dSng 2012)
Mot con lac 16 xo dao dpng dieu h6a theo phuong ngang voi co nang dao

-A

2

2

2

O

2

S ,.,.,=2A

3

b. Goe ma vat quet dupe trong thai gian — la:
;
4

i

A(p = ( o . A t ^ ^ I = i i
T 4

40

2

Gpi Q la dau co' djnh eiia 16 xo, khoang th6i gian ngan nhat giiia 2 lan

r-

lien tie'p Q chiu tae dung luc keo ciia 16 xo co dp Ion SVSN la 0,1s.

L
12

Quang duang Ion nha't ma vat nho ciia con lac di duge trong 0,4 s la
A. 40 cm.

B. 60 cm.

C. 80 cm.

D. 115 em.

'Phdn tich vd hu&ng ddn gidi
Nhan xet: Vi Id xo dat nam ngang nen luc dan hoi chinh la life hoi phuc.

Dehai

CO de cap den luc keo cua Id xo, ma luc keo cua 16 xo chinh la luc dan hoi vi the
ciingla

luc hoi phuc.

Theo bai ra, ta co h$ phuong trinh sau:

2

Ap dung cong thuc tinh S max t 3 CO I
Smax = 2 A sin ^

^3

—•

dpng la IJ va luc dan hoi cue dai la ION. Moc the nang tai vj t r i can bang.

2

= 2 A sin -

4

=

^kA2=l
AN/2

kA = 10

>A = 20 em.

41

^

T h o i gian ng§n nhat lien tie'p de
Fhp = —

2

.

Fhpm« la -

6

10

F

O

a

2
"2
„
I T
T
T
=> At = — + - . — = — + —
2

3 2
2
6
-

Goc ma vat quet d u g c t r o n g t h o i gian -

= 0,1 = > T = 0,6s

.
At 0,4
4
1
Thmg.an^ = - ^ = - = l + -

1 -10 *

j

Simax = 2 A sin ^

- 2 A sin —

S „ a x = 2 A + A V 2 = A ( 2 + V2)
Toe d g t r u n g b i n h I o n nhat ma vat d i d u g c t r o n g t h o i gian —
27T

T

= 2 A sin - I - ^ = 2 A sin - = A

|VTBmax -

-

+ >/2)^ A ( 8 + 4N/2)

37

-

3-^

Dang 6. Xac djnh thdi gian vat di dUoTc quang du'dng S
Day la bai toan nguac ve dang todn quang hwng

M p t vat dao d o n g dieu hoa v o i bien d o A va chu k i T. Toe d o t r u n g b i n h
3T
I o n nhat m a vat d i d u g c t r o n g t h o i gian — la
4

g A(4 + 4V2)
ST

^

4A(2-72)
' 3 7

'Phdn tkh ra hu&ng dan gidi

dang todn nay tht can gidi bdi todn xudi cho tot

m V i DU M A U :
Vat dao d g n g v o i p h u o n g t r i n h x = 4cos(87Tt -27i/3)cm. T h o i gian vat d i

^

3A(2 + 72)
4T

d u g c q u a n g d u o n g S = 2 + 2V2
A. 1/12

3T

Ta can xac d j n h q u a n g d u o n g Ian nhat u n g v o i k h o a n g t h o i gian tren.
, ^
3T
T
^
T
T
Ta co: At = — > — => At = — + —
4
2
2
4
T

c m ke t u liic bat d a u dao d g n g la:

B.5/66

C. 1/45

D , 5/96

^hdn tich vd hit&ng dan gidi
T a C O v o n g t r o n l u g n g giac m o ta chuyen d g n g eiia vat n h u h i n h ve:
t = 0 =>(p = - —

nen ban dau v a t 6 M .

3
T u M vat d i ve V T C B theo ehieu d u o n g

T
Q u a n g d u o n g ma vat d i d u g c t r o n g — l u o n la 2A.

Da d i d u g c q u a n g d u o n g 2cm.

3T
Q u a n g d u o n g Ian nhat ma vat d i d u g c t r o n g — c h i n h la q u a n g d u o n g I o n

42

than gian vl the de gidi tot

V i du 8: (Trich dethi thit truang chuyen Ha Tinh Idn 1 nam 2013):

De t i m d u g c toe d o t r u n g b i n h Ion nhat ma vat d i d u g c t r o n g t h o i g i a n

S = 2+2 x/2 t h i vat p h a i d u n g lai tai N

nhat ma vat d i d u o c t r o n g —.
4

;

V ? y chpn dap an A .

V l diJ 7 : (Trich Aethi thit truang chuyen Lam Son Thanh Hoa Idn 2 nam 2013):

3T

S _ A(2

la:

4

C h p n dap an B

A(8 + 4>/2)

"''

= AN/2

4

2

3T
V ^ y quan g d u o n g I o n nhat ma vat d i d u g c t r o n g — la:

Q u a n g d u o n g Ian nhat d i dugc : S^^g^ = ^ + Sj^^ax = 2 A + A = 3 A = 60cm

^

= 2 A s i n 4 r = 2A sin ^

-'Imax

T r o n g t h o i gian — q u a n g d u o n g l u o n la S = 2 A
+

la: A(p = co.At = — - = -

T
Q u a n g d u o n g I o n nhat ma vat d i d u g c t r o n g — la:
Simax

Q u a n g d u o n g Ion nhat vat d i dxxgc
T
t r o n g k h o a n g t h a i gian — la:
6

Cty TNHH MTV DWH Khang Vie I

Vay de vat d i d u g c q u a n g d u o n g :

/

2

4

^

i

1

4

/

Thoi gian: At = — + —= — ( s ) .
^
12
8
96^ '
C h g n dap an D
M
43


Bi quyet on luy^n thi dai HQC dat diem toi da Vat It, t4p 1-Le

V i d u 9 : (Trich. de thi thu truang chuyen Nguyen

Cty

V&n Vinh

Trai Hdi Duong

Idn 2

-IOV2
* r

-20

»

nam 2013):
Vat dao d o n g dieu hoa theo p h u o n g t r i n h x = 5cos(107rt - ^ ) ( c m ) . T h o i

1;

gian vat d i d u g c quang d u o n g 7,5cm, ke t u liic t = 0 la:

TNHU

o

Ml\-nWHKhau-^

\OsI2
r

20
•

f

r"

—s
15

C.

15

30

1
1

J

1

A.

•

1

J

D. — s

1

12

J

1
1
1

Cach 1: G i a i theo p h u o n g t r i n h l u g n g giac

/, ='0,5.v=>< x,=\0^f2cm
V,
>0

/,=6.v=J > <
V,

>0

V i (p = - ^ nen t = 0, vat qua VTCB theo chieu d u o n g , va A = 5cm nen khi
vat d i d u o c quang d u o n g 7,5cm t h i liic do v ^ t qua H dp x = 2,5cm theo chieu

Quang d u o n g vat d i dupe trong thoi gian 2,5T la: Sj = 2,5.4A - lOA = 200cm

am tuc V < 0, suy ra:

Quang d u o n g vat d i dupe trong thoi gian ^

2,5 = 5 c o s ( 1 0 T T t - - ) ^
^
2

c o s ( 1 0 n t - - ) = - = ^ 1 0 7 t t - - = - = > t = ^ = 4^
:
2
2
2
3
60 12

S,=2

A-

A>/2

= 2 20-

20 72

la:

= 40 - 2072(cm)

Cach 2: G i a i theo v o n t r o n l u g n g giac
V i t = 0 pha ban dau 9 = - j

Vay tong quang d u o n g vat d i dupe la:

nen vat ban dau 6 M .

S = S, + S2 = 200 + 40 - 20y/2 = 21 l , 7 ( c m )
T u M vat ve bien d i dupe quang d u o n g 5 cm.
De vat d i dupe 7,5 c m ke t u t = 0 t h i vat

C h p n dap an A

^

m B A I T A P VAN D U N G :

phai d i them 2,5 cm nua.

Cau 1. ( T r i c h de t h i dai hpc n a m 2013): M o t vat nho dao d o n g dieu hoa v o i
T u h i n h ve ta thay x = 2,5cm = — .

bien dp 4cm va chu ki 2s. Q u a n g d u o n g vat d i dupe t r o n g 4s la:
A. 8 cm

Vay t h o i gian can t i m la:
tMN = t

(0->A > A

,=W)+t^^

B. 16 cm

C. 64 cm

D.32 c m

'Phdn tich ra huang dan gidi

-1 + 1-.^ = J-S
4 ^
^2 12

At
4
So chu ky vat dao d o n g trong 4s la: N = — = — = 2

C h p n dap an D
vi d u 1 0 : (Trich de t h i t h u chuyen Le Q u y D o n - Q u a n g T r i Ian 1 n a m 2013)
M o t chat d i e m dao d o n g dieu hoa v o i p h u o n g t r i n h : x = 20cos Trt

cm
4

V i so chu ky vat dao d o n g trong thoi gian 4s la so n g u y e n N = 2 nen quang
d u o n g vat dao d o n g trong 4s la: S = N.4A = 2.4A = 8A = 8.4 = 32cm

C h o n dap an D
Cau 2: ( T r i c h de t h i t h u c h u y e n Quoc Hpc - H u e Ian 2 n a m 2013)

(cm,s). T i n h quang d u o n g vat d i dupe t u t h o i d i e m ti = 0,5s den t2 = 6s ?
A . 211,7 c m

B. 201,2cm

C. 101,2cm

D. 202,2cm

^hdn tich ra huong dan gidi

Mot con lac 16 xo dao dong dieu hoa v o i p h u o n g trinh: x = 10cos(TTt - ^ ) c m .
Quang d u o n g vat d i dupe trong khoang thoi gian tir ti = 1,5s den t2 =

s la

Theo bai ra, ta c6 h i n h ve m o ta chuyen d o n g cua vat n h u sau:
L a p t i so:
^

lizii =^IlM
T

2

= 2,75 = 2,5 + 0,25 =^ t j - 1 , = 2,5T + ^
^

4

A . 5 0 + 5V3 (cm)

C. 50

+ 5V2

(cm)

B. 40 + 5N/3 (cm)

D. 6O-5V3 (cm)
45


Bf quyei

on luyfit

thi dai

UQC dat

diem

toi da Vat It, tap

1-U

Van

VmR

m

i'hdn tick vd hudng dan gidi
Cach 1: G i a i theo p h u o n g p h a p dai so

n

^gu
1,571
V

—

2y

=0

Xi3 =10cos

N =

At

71^

U

2

— 7t

(13
V ] 3 =-107tsin
13
^ T

17

T

7t

= 5V3cm
Tl\

^
, , 2 T
T
Ta co: At = — > —
3
2

17
12

12

Q u a n g d u a n g t o n g cong vat d i dugc la: S^t = ^nT + S^,' =

12
+ S5J
12

V o i : ST = 4A = 4.10 = 40cm.

^13
3*

2

-

Vay: S^t = SnT +

^AV

-

Xl,5

5V3-(-10) = 5 7 3 + 10 (cm)

= 40 + SVS +10 = 50 + 573 (cm)

Cac buoc dau giong each 6 tren, chi

Simax = 2 A s i n ^ = 2 A s m - = A
\^
Slmin = 2 A 1 - c o s —
2 A + S,

= 2A

1

^

1-cos —
6
2A + A

= A(2-73)

3

2A + A ( 2 - 7 3 )

4-73

C h p n dap an D
Cau 4: ( T r i c h de t h i t h u T H P T Phiic Trach - H a T i n h Ian 2 n a m 2013)

khac 6 vi?c t i m S^t'
Goc quay duoc t r o n g khoang

M g t vat dao d g n g v d i p h u o n g t r i n h x = 472cos

cm. Quang duong

5T
12

27t 5T
ã Ao) = â.At = .
T 12
46

c h i n h la

Goc ma vat quet d u g c t r o n g t h o i gian — la: A(p = oo.At = — — = —
6
T 6
3

Cach 2: S u d u n g v o n g t r o n l u g n g giac

t h a i gian A t ' =

T
T
At = — + —
2 6

quang d u o n g Ion nhat va nho nhat ma vat d i d u g c t r o n g — .
6

_S^3,

C h p n dap an A.

-

4-73

Qu an g d u o n g Ion nhat ma vat d i dugc t r o n g — la:
6

0

At
D.

2T
Qu an g d u a n g Ion nhat va nho nhat ma vat d i dugc t r o n g —

12

5T

-

Vi

2

'Phdn tick vd hu&ng ddn gidi

2J

Vay t h o i gian vat dao d o n g la T va A t ' =

>

C.1

B. (2+ 72)

A. 3

>0

-

fVi5Vi3

3: ( T r i c h de t h i t h u c h u y e n N g u y e n H u ? - H a D o n g Ian 2 n a m 2013)

Quang d u o n g ma vat d i dugc trong — l u o n la 2A.

13
-1,5
_ 3

6.2

J

— =

(cm)

At = 2T/3 la

(13

So chu ki dao dpng:
tl3-ti,5

+ 1 0 = 50 + 5 7 3

Ian nhat so v o i quang d u o n g nho nhat vat d i d u p e t r o n g khoang t h a i gian

=> Vat di qua vi t r i x = sVScm theo chieu duang.
-

SAI' = 4 0 + 5 7 3

MQt vat dao d p n g dieu hoa v o i bien d p A , chu k i T. T i sogiiJa quang d u o n g

=> Vat d a n g bien am.

Tai t h a i d i e m t = ' I (s)

= Snx +

nhanh chong. 0 day bai todn duoc gidi theo edch true quan, dua vao hinh ve.

Tai t h o i d i e m t = l,5(s)
V|5 =-1071 sin

-

SAI

N h ^ n xet: Cdc ban cd the su dung 3 each neu trong bai VI DU MAU van gidi ra
5 =10cos 1 , 5 . - ^ = -10cm

-

Vay:

C h p n dap an A

C h u k y dao d p n g : T = — = — =2(s)
CO

f'Dya vao v o n g t r o n ta c6 quang d u o n g S^t' = 10 + 5 7 3

,

, 57t
A(p = —
6

v^t d i t u t h o i d i e m t , = —s den t j = 6s la

'
10
^
A. 331,4cm.

B. 360cm.

C. 337,5cm.

D . 333,8cm.
47