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m m+

R
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R
m m+
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1
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R
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R
k
m m+

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!T
R
!"R7%
8K(K-
1
!1.(M-
"
!X'1Aa-!L"bc72ri
A)'%MA))<lZ23CK`B\
@A51'L?Alag8K;/dZ2
fg8!O'n7%
"
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K21O'ncWR'"c M2bRcWXR'"c N2LRcWXRc P21"RcWnRc
h€•€
U∆l!
1
7!R'R1bLn‚K
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Uc
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_45!T([g
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R
A
:;<j2ri(
bRR
E
m g
=
A)M;/d(.
R
1 7v m s=
2h+>5))
))?)y8)Y9-)`g2^5(
))-)45)49,/0)1RR)nR2N
"
1R 7g m s=
2M/5)

R
b 2A cm=

2
R
1R 2A cm=
2
R
b " 2A cm
=
O
R
b EA cm
=
2
K
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t
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c
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c
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SK

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U5))))?
 ;sfM /0DU!
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R
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M m+
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U^5KV!$1RR6nR&"!1R
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b E21RA m

=
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Z!1RRc72M,(/0Fu%lA>
52NFu89Z/.l(.,.!7b
!"'R7%
"
2^Y`FuA
b2 X2 1R2 OL2}
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R
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la ∆2"
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aZ!"Rc7Z',/.B',
1F„`./0!LRR'(`./0!"RR/0+dH!
"R%„'(`5„IA,'5))
l)?2N:!R8I5'.:5B\@A=i(U'
/d/.2m/d=i()2

E
 "R "%$b &
X
π
= −
 
E
 1R "%$b &
X
π
= −

 1R "%$b &
X
π
= +
O
 "R "%$b &
X
π

= −
K
U3…-„5F@AC
1



∆ =

U3-iUB\@ACW
"
$ &


+
∆ =
U3+85iU[
R " 1

  

= ∆ − ∆ =
!1R
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h66j p e" +6Y6d5"6 42.i# !j q 5rKk+
&=
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&=
+
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@
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@77
K N'A,)/ABA>5'(-./0

1
!R'b-Z!"Rc72(-./0
"
!R'b89:;<
=.
""
b
7%>5(
1'
%5ABC52ri%.
%F/0G())R'12fg8!1R7%
"

2 .45=(%,
CZg)

""
b
7% ER7%2 J O1R
E
7%2

1'bcm
x

]
]

(

(

(

P(5(.(%5
sm
mm
mv
V 7
1R
""
=
+

=
DB\@ApFB\@A{5
m
k
Mg
k
F
x
ms
Rb'R===
µ
$!"&
3(B\A(FB\@A{15
sfA+)dp
mAAAAFMVkA
ms
RLL'RR11'R1R2
"
1
"
1
"""
=→=−+→+=
D(.=(%k5FB4*B\@A2 ;,A)%,C,
Z)(B\g)B\@A%k5.45
N1%†<A+)p/0
scmvvxAFMvkxkA
ms
71b'QxR1L'Rxb'RRb'R21RRLL'R21R&$x
"

1
"
1
"
1
""""""
=→++=→−++=
N"-9*B\@A%†
NZ%17XA+,8D MD NM-4
i17X>;A)KV!KS!R'RLLSR'Rb!R'R1L
.45)
scmA
M
k
Av 71b'QR1L'R2"Rxx2x ====
ω
3flA>-,[@l/lg8FF2N-9/y
JK?a'Z!bRc7'
,.B',(`./0
1
!1RR2M,G(
1
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1R'(`F./0
"
!XRR%F(
1
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:;/d=<2ri%.%F/0GF(µ!R'Rb
fg8!1R7%

"
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"
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k
mm
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+
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WNl=4%FK
t
!µ∆!R'R"b$w&
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"
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<=4%F.
"
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"
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"
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7

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IKNdi/A2M>!1'n'aZ!1RRc72(.

/0!"RR89.
R
!b7%>)$A,Z8&;<=
2ri%.%F/0G))•!R'"2N5)))?
8@2 .45=%ABC45)
K217% M2R'nnL"7% N2R'XOOX7% P2R'X"1"7%
h+/%
\(.(%5(
M+)/0)A+)p
!DSV
bOx
−=→
Vv
smVVV
mvMVmv
71&bO$Ob
"
x
""
"""
"""
=→−+=→+=
DB\@AFB\@A{5$C\C&
t

!t
%

==→
k

mg
x
µ
R'REL!E'L
3(\\CgFD NM{15
mAAAAFkAMV
ms
1RE'RL'EbRO'R2
"
1
"
1
"""
=→+=→+=
.45%,C,BB\@A/0\
smxA
M
k
xAv 7XOOX'R&REL'R1RE'R$
n'1
1RR
&$&2$ =−=−=−=
ω
r-9%†<A+)p/09\
&2222222$
"
1
"
1
"

1
"""
xAFmvkxkA
ms
−++=
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"
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"
2hFB`g=9
(M-9Y/Y)B89)
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Ksi9(M-9Y/Y)B89)
K
1
≥µ
"
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1
≥
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gm
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µ
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1b
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oK!
k
gmm &$"
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h:
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1
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R
!SSSST!1R
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kA
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K
R

K
1

j
KN
M
h+
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M=%5
" "
X X
" " " " "
 


" " E
 
1 1 1 "'b21R "'b21R
Kx K  K x K K "'b L'"b L'"b L'"b 1"'b
" " "  $"R & X21R
= + ⇒ = + = + = + = + = + =
ω π

!"'b
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=
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E " E E2R'1
  
X n n
π π
∆ϕ = = ω = ⇒ = =
!R'REQb%
r
1
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%!R'13'

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KR'Ob7%MR'E7%R2Ob7%PR2E7%
K ;B(A+)p/0'-K
mgS
mv
A
mv
mv
Fms
à
+=+=
"""
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v
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OXOQ'ROR"'R12R2n'O2Rb'R2"1"
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7%
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mv

mgA
kAmv
A
kA
Fms
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à
SSSSST"RK
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Một con lắc lò xo gồm vật m
1
(mỏng phẳng) có khối lợng 2kg và lò xo có độ cứng
k=100N/m đang dao động điều hoà trên mặt phẳng nằm ngang không ma sat với biên độ
A=5cm.Khi vật m
1
dến vị trí biên ngời ta đặt nhẹ lên nó một vật có khối lợng m
2
.Cho hệ số
ma sát giữa m
2

và m
1
la 0,2; lấyg=10m/s
2.
.Giá trị của m
2
để nó không bị trợt trên m
1
là:
A.m2>=0,5kg B.m2<=0,5kg C.m2>=0,4kg D.m2<=0,4kg
h+^
"

1
i,%.-!
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mm
k
+
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mm
k
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s9
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1

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si9
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K
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g
mm
kA
à

+
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@(# [".$:$"
BMột con lắc lò xo gồm vật nhỏ khối lợng 0,2kg và lò xo có độ cứng 20N/m.Vật nhỏ
đợc đặt trên giá cố định nằm ngang dọc theo trục lò xo.Hệ số ma sát trợt giữa giá đỡ và vật
nhỏ là 0,01.Từ vị trí lò xo không biến dạng truyền cho vật vận tốc ban đầu 1m/s thì thấy con
lắc dao động tắt dần trong giới hạn đàn hồi của lò xo.độ lớn của lực đàn hồi cực đại của lò
xo trong quá trình dao động là:
A. 19,8N B.1,5N C.2,2N D.1,98N
h+h:K)A45=23-4)?45=*F
lt

!K
s9K54)sfA+)p/0
mgA
kA

AF
kAmv
ms
à
+=+=
"""
"""

8%.Wg8!1R7%
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81RRRK
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K!
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. &=
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2
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h+!R'R"W!1c7Wà!R'1W!1R7%
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R
!
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kA
!R'RR"w2
c>(D NMl=4%FK
%
!àK!R'RR"w
c/58g8(l9/0*/0D NM
h+%(H5[B\FD NMj5'
-;sfA+)p/0-

"
"
kA
!
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kx

Uà$KS&SSSST
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kx
Sà!R
R'b
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}
1
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t

!!R'RXcTt
%

!

à!R'R"c2P-(89>D NM2
}
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!R2 )Ap/0A,_A>)l=4
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[".$:$"

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KZ?a-Z!1RRc7'1,.B'
1,(./0!R'b2M,C(;/dZ`
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=4+-A171RR:4F<(2NA=(+
Hz'g8!1R7%
"
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)
K2"b M2bR N2Qb P21RR
h+h:∆K)+AŽ,(*D NM

&x$R1'R
"
x
&x$
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x
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"""
AAmg
kA
AAF

kAkA
c
++=++=
&x$R1'R&x$
"
x
"
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AAmgAAF
kAkA
c
+=+=−
&x$R1'R&x&$x$
"
&x$
"
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AAmgAAAA
k
AA
k
+=−+=−
;;;;<∆K!K6KV!
mmm
k
mg
11R
1RR
1R2b'R2R"'RR"'R
E

===

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