CÁC DẠNG TOÁN THƯƠNG GẶP VỀ DAO ĐỘNG
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Loại 1: VIẾT
PHƯƠNG TRÌNH DAO ĐỘNG:
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Loại 2: CẮT - GHÉP LÒ XO
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2
P$DW2Y2T$QRT2$2jV0$5/S,-D>Ie2
2!2J3%$,-DW‚D;
&π#$%
4Qπ#$%
(Q
π
#$%
?QLπ#$%
Câu 20:#<52#!%$,-,'5`$P$DWD`.2!
A. ;,-I2^25J;U2J3/2J3,Oj,62J3%$,-Q
B. $5"‰DJ12,ƒ'5/O2T,X"2>,Oj$DJ,-Q
C. G,-2/8";ED>/G,-8"2!2Q
D. P$12Ie,-G12,ƒ'55VX,-Q
Câu 21: _-2DWD`.%$,-,'5;a2#!
SL
x t cm
π
π
= −
Q42G3DEP$
<58J5D;QRDE%$,-P$12D; A.
/L J
B.
/L mJ
C.
/L mJ
D.
/L J
Câu 22:_-212%$,-,'5;/0$5"-2G82T$/S2!,-D>Ie2QJ3
%$,-P$12D;A./gmB./SgmC.SgmD.gm
Loại 3: NHỮNG BÀI TOÁN LIÊN QUAN ĐÊN SỰ BIẾN THIÊN CHIU KỲ GIÁ TRỊ NHỎ.
Dạng 1: biến thiên chu kỳ con lắc đơn theo độ cao:
$23:"2,j2"2IX
M
g G
R
=
$23:,-$
M
g G
R h
=
+
#,O
_D;G3DEP$2#,j2
e3j%Š
‹IG]2#,j2
tAI2^5Gb:,-$
T T
T h
T T R
−
∆
= =
#$
F
F
9
o&
F
2
F
Œ
F
2
Dạng 2: Biến thiên chu ky ở độ sâu:
o3DEP$2#,j2:,-d5;2d"
ˆ
R h
M M
R
−
=
÷
$23:,-d5
( )
( )
Q
ˆ
ˆ
M R h
M
g G G
R
R h
−
= =
−
(5GVI2^2Y,-d5
ˆ
ˆ
T T
T h
T T R
−
∆
= =
Dạng 3: Biến thiên chu kỳ theo nhiệt độ:
('5%;P$%dV2#Y2YH2,-2
( )
l l t
α
= +
#,O
l
'5%;%dV:
(
α
H3:%;o
c
l
'5%;%dV:2
(
(620J,)g'2"X5
42^5Gb
T T T
t
T T
α
− ∆
= = ∆
Dạng 4: con lắc chạy sai trong một ngày đêm.
426202]5GbP$DW,qq2#2#TE>V,)
;>V$
4@12•3
%U620J,)5J
R5
~5V#$,qq>V$
R5
}5V#$,qq>V1"
4]3%$,-";DW,qq>V$2AH,E2#;V,^"
29ZL
t
N
T
=
4L]2T$,qq>V$
ˆ
T
t NT t
T
= =
4ST$>V$
( )
ˆ
T
t t t t
T
∆ = − = −
(DW,%UD;"DW,qq2T$,qq>V$2#;V,^"
ZLk
T T
t
T
−
=
2#,O
5GbDW>V,)w
5GbDW>V$Q
Loại 4: CON LẮC ĐƠN CHỊU TÁC DỤNG CỦA LỰC LẠ
R;2#+DA;DA2!DW,E,22#"62#G$5
[(D,>22#,H2#TN52%BP$DA,H2#
F qE=
r r
[(DW,22#H5VX,-O$23.Y/2$"$V•52Y"DB<52]
f ma=
r
r
22#+DAIX5Gz9[f
MY"DWD);VDWI!2Ta5Gb
ˆ
ˆ
l
T
g
π
=
z$23IX5G^
a,E.,
ˆg g a= +
r r r
#$
()*
( )
ˆ
ˆ
ˆ
F P g g a g
F P g g a g
F P g g a
↑↑ ⇒ = + >
↑↓ ⇒ = − <
⊥ ⇒ = +
r r
r r
r r
Loại 5: VẬN TỐC VÀ SỨC CĂNG DÂY
d23
c v gl c
α α
=
123A,>
"$. V gl c
α
= −
:(4
@A%dV
T mg
α α
= −
\(4DAA,>
$. Tm mg
α
= −
#TE
9c
c
α
α α
<
123
v gl
α α
= −
@A%dV
V. TỔNG HỢP DAO ĐỘNG
1.ƒE$%$,-,'5;UU2J3.
9&
ω2[ϕ
;.
9&
ω2[ϕ
,E
"-2%$,-,'5;UU2J3.9&ω2[ϕQ
#,O
A A A A A c
ϕ ϕ
= + + −
2$
A A
A c A c
ϕ ϕ
ϕ
ϕ ϕ
+
=
+
aϕ
ŽϕŽϕ
5ϕ
Žϕ
kR5∆ϕ9Gn.
/.
U$⇒&
_$.
9&
[&
•
kR5∆ϕ9G[n.
/.
E$⇒&
_
9|&
c&
|
⇒|&
c&
|Ž&Ž&
[&
2.oI2"-2%$,-2;J.
9&
ω2[ϕ
;%$,-2ƒE.9&ω2[ϕ2!%$,-
2;J`D>D;.
9&
ω2[ϕ
Q
#,O
A A A AAc
ϕ ϕ
= + − −
2$
A A
Ac Ac
ϕ ϕ
ϕ
ϕ ϕ
−
=
−
aϕ
ŽϕŽϕ
5ϕ
Žϕ
3.R5"-2122$"$,q2T'5%$,-,'5;UU2J3.
9&
ω2[ϕ
w
.
9&
ω2[ϕ
•2!%$,-2ƒE‡D;%$,-,'5;UU2J3
.9&ω2[ϕQ
(5D^2#B•.;2#B•V⊥•.Q
$,E
QQQ
x
A Ac A c A c
ϕ ϕ ϕ
= = + +
QQQ
y
A A A A
ϕ ϕ ϕ
= = + +
x y
A A A⇒ = +
;
2$
y
x
A
A
ϕ
=
aϕ∈‘ϕ
_
wϕ
_$.
’
Dạng 11: Tổng hợp hai dao động cùng phương cùng tần số
#$
Câu 1: _-2122$"$,q2T$%$,-,'5;U/O2#!DJDE2D;
.
92cπ "w.
9L2[π Z"2,IedVQM,N123A,>P$12QA. S"
B. S" C. S" D. S"
Câu 2:_6
“
2d
“
22
“
^
“
,6
”
2
”
L%$,6
“
,^
”
5
”
$5
”
$
”
5
”
2d
”
6
•
•
$
•
2#–
”
.
9π2[π"w.
9π2"w.
9π2[π"w.
L
9π2"Qg$
—
V.$
•
,
“
2#!%$
,6
“
26
˜
“
5
˜
$d
“
2A.
S
ππ
+=
tx
B.
S
ππ
+=
tx
C.
S
ππ
+=
tx
D.
L S
ππ
−=
tx
Câu 3:g$%$,-,'5;OU;U2J3f9Sgm/OI^,-DJDE2D;$;$/$
I$,J5DJDE2D;π ;πQ2#!P$%$,-2ƒEO2XD;2#!;$5,dV
A.
x a t
π
π
= +
÷
w B.
x a t
π
π
= +
÷
w C.
x a t
π
π
= −
÷
w D.
x a t
π
π
= −
÷
w
Câu 4.g$%$,-2;JOI^,-L";"Q4^,-%$,-2ƒEO2X12#N
A.L" B.L" C." D./S"
Câu 5.(OI3%$,-,'5;UU2J3OI^,-;$I$,J5D;&
9"w&
9Z"w
&
9L"w&
L
9";ϕ
9wϕ
9π wϕ
9πwϕ
L
9π Q4^,-;$I$,J5P$%$,-2ƒED;
A.
L w
L
cm rad
π
B.
L w
L
cm rad
π
C.
L w
L
cm rad
π
−
D.
L w
L
cm rad
π
−
Câu 6:_-212%$,-,'5;0$5 2!,-D>Ie2Qs5h,T12,,E
2#/SD;Z"Q(+32T$D)12<5$N2#]dIe2Y'5d"Q2#!%$,-P$
12D;
A.
x c t cm
π
π
= +
w B.
x t cm
π
π
= −
w C.
L L
x c t cm
π
π
= −
w D.
L L
x c t cm
π
π
= +
w
Câu 7_-2122AH,q2T$%$,-,'5`$U2Y2#!$5.
9L
t
π α
+
";.
9
L t
π
"Q4^,-P$%$,-2ƒEDaj2
A.
π
α
=
#$% B.
π
α
= −
#$% C.
α π
=
#$% D.
α
=
#$%
Câu 8:_-2122AH,q2T$%$,-,'5`$U2Y2#!.
9cL
π
2;
.
9L
π
2"2#!%$,-2ƒED;
A. .
9
π
2[
Z
π
"B. .
9
π
2c
Z
π
"C. .
9
π
2c
Z
π
"D. .
9
π
2[
Z
π
"
Câu 9:g$%$,-,'5`$;U/U2J3;UI^,-&9L"Q>"-22T
,X";,O/%$,-OD,-.9"/,$5VX,-E'5%/`%$,-,<5$N
2#]dIe2Y'5%Q@),O/%$,-2ƒEP$$%$,-2#^OD,-I$^5;,$
5VX,-2Ya;K
A. .9";5VX,-E'5%Q B. .9;5VX,-E'5%Q
C. .9L";5VX,-2Y'5%Q D. .9";5VX,-2Y'5%Q
Câu 10:_6
“
2d
“
22
“
^
“
,6
”
2
”
L%$,6
“
,^
”
5
”
$5
”
$
”
5
”
2d
”
6
•
•
$
•
2#–
”
#$
