


( Đề thi gồm có 02 trang)

 !"#"$!"##

%&$
#'"()*+(không kể thời gian giao đề)
#',!,!"##
 #/(3,0 điểm)

 !"#$%&'
(
v
uur
)*&+,
- /0 12314
56)*78!9:;<%;=:>;
?@AB!BC'D>;<4
EF0)-GHD !"#$%
&'H !IG&4&B'JKGC'@
L55#)
 !/(2,5 điểm)
<A5#>?@>&B!H
5%A3M
F

N
HD!3M5  E
N0)* 5O>K>*H@P5%A3M5#&4

'LQ5#A#3,)R8'L
8ANS
(
*E @B 5O>K>*H
D#31@ATA#>UA#FA#)V'HW8
L8 !IE HI!#X&4)6"
HY
Z
K
[NY
Z
*
)-\< I8D#Y
Z
O
@
8)
 0/(3,0 điểm)
*:83EU)
!H'88!,!L']^
F
[^
N
[_Y>!
F
[F`>!
N
[N`a:Hb
F
[T`>b

N
[S`
8!,ba5+Ycd>TY)efg8C':H
h'3Eia5+H8!,!A)#
Fj-8'8+k
OK
 !I8!,b)
Nj*'8''Ll'])
 1/(2,5 điểm)
-'5#G;
F
>;
N
!55#>H
9AA3Mm
F
>m
N
 '5lQ!9#)
$?GOK!3'5#;
F
 ES0>
3M%H:'%QC'8A5
F
)eP$%
I>nn'5#E%H:C'8A5
N
)
FjE8@AB8Pm
F

>m
N
>5
F
>5
N
l)
 NjK+5
F 
[F>5
N
[S>l [NT'5#!BA
&4QH+'a3M:&,
?o'A]& 5#'L;
N
A
F>NTA& 5#'L;
F
)# 9m
F
m
N
)
!FjN

-EF
-EN
-EU
-ES
 2/(3,5 điểm)

*:83ET
( )
OK
' [k Np Y
>
p
n3M>
N
6
b [
*
)
Fj*@!48 ' 5+'
')
NjY8%'L:>%
p
H !I
A
F
p

N
p

0E8@AB8P
F
p

N
p

)
&0E8%'L:&+%cL
5+
F
Y
>
N
Y
AA3MA
F
k

N
k
)
qg9
F>_
6[ -
r
a
sU
F(
*[ t
ur
a
F
k [FT(Y
a
N
k [N((Y)

KGC'8!,gX%>8!, 5+!A)

 3/(3,5 điểm)
*A<6Hh'gvB
(
STl cm=
$GH5%
A3M
 F((g=
>5#3$5 5D)
Fj!2A<231?@>'!B%I>'g3!2$>5
X&4>A<Hh'g
T(l cm
=
)E@LA<)
Nj*=A<
F
6
>
N
6
Hh'gAA3MA
F
FTl cm=
>
N
U(l cm=
!]="231?@!2$3E_)OKA
D%I):D&'>P$A<5&+g:>
'Hw$g)

0*@$gh')
&0Y+31!Eg.7%AA" A<5&I
&+g:>%7,I!#X&4>h'g313<'%0)
0#AvAG g9ABDK)
6
N
F( jg m s=
&GC'7 )

 4/(2 điểm).
ef2Ag'x!9 '<'%A:QHLE+
8< I$$!'&E!BH)-G 2+3+>+'
3!HMgXHh'g\&+>C'g7]]&XJ* 2x
\&+!3h'g3<#:LH!35: <'%)
$$$$$$$$5$$$$$$
-7B7)))))))))))))))))))))))))))))V%& g)))))))))))))))))
e IF)))))))))))))))))))))))))))))))))))RyB)))))))))))))))))))))
e IN)))))))))))))))))))))))))))))))))))RyB)))))))))))))))))))))
-ET
-E_

z-{*N(F(sN(FF
678
%&s-|
F}j(NjN(FN
9 6:;$678 <=>
 #
?0@"AB
s*78!9:;<%;=:>;?@AB!B
C'D>;<43Ei)

se7
α
AHM&,
(
v
31)
s|31!E'DL 
( )
(
N
(
.F0
 .N0
N
x v co s t
g t
y h v t
α
α
=



= + −


s|31!EC'~:L 
[•<
α
s

N
N
N
(
N
x
scov
g
α
.U0
sR!"#



=
=
Hy
Lx
.U0
3M6
N

N
α
sN
(
N
6
α
•6

N
•N
(
N
o0[(.S0
€D31!E.S0A'H8
α
E
•
∆
≥
()
-
(
S
oN o0
(
N
o
N
6
N

≥
(
V'!
(
N

≥

‚ o0•
NN
0. LhH
+−
ƒ
Y$
( ) ( )
{ }
N
N
(
 g H h H h L= − + − +

(>T
(>T
(>T
(>T
(>T
(>T
 !
?!@2AB
„8&'
(
H

F
[.
K
o
O

0V.0

N
[.
*
o
K
0V.&0

O
Y
O
[
K
Y
K
[
*
Y
*
[b
(
.0
(>T
!Fj_
6.0.&05+M.03M
F
N
 F
 T

=
 .F0
„8A"'H

F
[.Z
K
oZ
O
0V.g0

N
[.Z
*
oZ
K
0V.20
Z
O
YZ
O
[Z
K
YZ
K
[Z
*
YZ
*
[b.…0

6.g0.205+M.…03M
•
F K
•
N O
 Y
F
 Y
= −
.N0
.F0.N0
•
K
•
O
Y S
Y T
=
K+YZ
O
•YZ
K
•YZ
*
[uA#
#3M
• •
O K
ST U_
Y † Y

FF FF
l l= =
qg931!E!: 5#A#3,5O,!: '
'
• •
O O O O
(
 Y  Y
 
=
Y.
K
o
O
0V[.Z
K
oZ
O
0VV'!
•
O
O
 }
 U
=
R+C'[_S}R
(>NT
(>T
(>NT
(>NT

(>NT
(>NT
(>NT
 0
?0@"AB
FjH‡[‡
F
•‡
N
.F0
qg9IA'$; ::@']
k
OK
[^
F
o‡
F
.!
F
•b
F
0.N0
k
OK
[^
N
o‡
N
.!
N

•b
N
0.U0
k
OK
[‡b.S0
V'!‡
F
[‡
N
[
‡
N
2h%c5+Ad>T.Y0)H
k

[k
K
•k
K
!Hk
K
[^
N
o‡
N
!
N
[^
N

o
‡
N
!
N
k
K
[‡
F
b
F
[
‡
N
b
F
)
V'!k

[^
N
o
‡
N
!
N
•
‡
N
b

F
[_•F>T)‡[d>T
Y$‡[FOa‡
F
[‡
N
[(>TO
R+C'k
OK
[^
F
o‡
F
.!
F
•b
F
0[U.Y0
2.S0#3Mb[U`)
Nj*'Ll']8
|
F
[^
F
‡
F
[Uˆa|
N
[^
N

‡
N
[Uˆ
-8'' ']8
-
F
[
F F F F
F F
k ^ ! ‡
uF>d‰
^ ^
−
= =
)
-
N
[
N N N N
N N
k ^ ! ‡
}U>U‰
^ ^
−
= =
)
(>NT
(>NT
(>NT
(>NT

(>NT
(>NT
(>NT
(>NT
(>T
(>NT
(>NT
!Nj_
 1
?!@2AB
Fj!3M;
F
!3;
N
g
F
[<H
•
F
F
F
<…
g
<s…
=

•
F F F
N F
F F

<… < … <…
g g
<s… <s…
l l
l l
− −
= − = − =
V%Hg:L8
F N F N
F
F N N F N F F N
… … … …
5 )
<s… g s… <. … … 0 … … …l l
   
= − − =
 ÷  ÷
− − − +
   
V'!5
F
<.lo…
F
o…
N
0[5
F
l…
F
o5

F
…
F
…
N
•…
F
…
N
.F0
31v!3M;
N
,!3;
F
H
5
N
<.lo…
F
o…
N
0[5
N
l…
N
o5
N
…
F
…

N
•…
F
…
N
.N0
*.F0.N0'D5f<&+n3M
5
F
5
N
A.…
N
o…
F
0[…
F
…
N
.5
N
o5
F
0
R+C'm
F
om
N
[
N F

F N
5 5 F
)
5 5 l
 
−
 ÷
 
Nje7bA& 5#'L;
F)
Y& 5#L'L;
N
A
F>NTA& 5#'L;
F
H
m
F
[.oF0
F
b
m
N
[.oF0
F
F>NT)b
c%
F
N
m

F>NT
m
=
.U0
 %A8'hm
F
om
N
[U.S0
e8.U0.S03Mm
F
[FTgm
N
[FNg
(>NT
(>NT
(>NT
(>NT
(>T
(>T
(>T
 2
?0@2AB
Fje7HA8P8 L:O*>*Kg8AA3MA
F
ϕ
>
N
ϕ
F


C
Z
R
ϕ
−
=
>
N

L
Z
R
ϕ
=
⇒
F N
N N
  F
C L
L
Z Z
C
R R
ϕ ϕ
−
−
= = = −
⇒
N8 '5+'')

Nj
0H
( ) ( )
N N
N N
F N
F N
N N

F F
N N
R R
R L R L
C C
ϕ
ω ω
ω ω
= =
   
+ − + −
 ÷  ÷
   
N N
F N
F N
F F
L L
C C
ω ω
ω ω

   
− = −
 ÷  ÷
   
( )
( )
F N
F N
F N
F N
F F F
(
F F F
(
L
C
L
C
ω ω
ω ω
ω ω
ω ω

 
− − − =

 ÷
 

⇒


 

+ − + =
 ÷

 

(>dT
(>NT
(>NT
(>NT
.A:0
Trang 4/6
!Uj_
F N
F N
F N
F
(
F F
L
C
LC
LC
ω ω
ω ω
ω ω

+ =



⇒

= → =


&0sH
N N N
FR C
U U U+ =
>
N N N
NR L
U U U+ =
>
N
L
R
C
=
N
L C R
U U U→ =
S
N N
F
N N
N
R

R
R
U
U U
U U
→ + =
−
( )
N
N N N N
N F N F
)
R R
U U U U U U→ = −
→
F N
N N
F N
R
U U
U
U U
=
+
s5 
N N
F NAB
U U U= +
F N
N N

F N
N N
 (>u_
R
AB
U U U
U U U
ϕ
→ = = =
+
(>T
(>T
(>T
(>T
 3
?0@2AB
Fj
•:Y*K
(
dh
P F+ =
ur uuur r
⇒
mg k l= ∆
N( jk N m
⇒ =
Nj
•e7
F
k

>
N
k
A @L A<
F
L
,
N
L
- Tại Y*K;
dh
P F=
( )
F N
mg k k l⇒ = + ∆
( )
F
l CO AC l∆ = =
A.\0L
N
L
(
F
L
)
sY$,YHAx
. 0x OM=

d
P F ma− =


F N
P F F ma− − =
( )
F N
••k k x mx⇒ − + =
*@G$gh'%H
F N
k k
m
ω
+
=
.0
N&j
•|31!EgHg:
( )
x A t
ω ϕ
= +
•+' g9 A<
F
L
,
N
L
QAvtE
F F N N
F k l k l k l= ∆ = ∆ = ∆
>

F N
l l x l x l x∆ = ∆ = ∆ = ∆
.
x
∆
A&+g:@
1Ih'gLA<0
(>T
(>NT
(>NT
(>NT
(>NT
(>NT
O

C
;
K
F
F
uur
N
F
uur
Trang 5/6
!Sj_
F F N N
kl k l k l⇒ = =
F
_( jk N m⇒ =

>
N
U( jk N m=
mH
F N
U( j
k k
rad s
m
ω
+
= =
sEO
ϕ


( )
F N
mg k k l= + ∆
.F0
F N
(>(FFF
mg
l m
k k
∆ = =
+
:[(6<5&+g:>@,*H7
(
x


(
F>FFx OC l cm= − = −∆ = −

(v
=
V'!
F>FFA cm=

ϕ π
=
Y$
( )
F>FF U(x t
π
= +

Nj
•6vG g9ABK5$,*

(F =
•6vA g9KA5
N
L
&I:
< N
)N (>__dF k A N= =
(>NT
(>NT
(>NT

(>T
(>T
 4
?!@"AB
s6A= 7&4MgXC'!7)mQ]]&
X< I'5ELA=)V'H>gQ@A=>HD< 
I3M
Š
g
s%!7!3LA:
N
Š
N
S l
g
T
π
=
,Xh'gALA=\3M!3
s2IA'$g‹x!9
Š
Š
N
P M
g G
m R
= =
M A5%A3ML>R A& 5#LHGA4%g‹
x!9)
s*+L31!E!B&4'3M

N N
N
S R l
M
GT
π
=
sK 5#L&D'gŒC'h'g<#:CL
N
C
R
π
=
(>dT
(>NT
(>NT
(>NT
!Tj_
sb"!5%A3M!B!'&ED L
N
N
_M l
D
V GT C
π
= =
H#m)
(>T
C)*D/
 ! "#$%&

'( )* !"+,(- )*',(. /012$3456 
7 )892$! "346 &
:'( "2" ;<' => '',(.(!?1
@ '(!>,(63A! B"C( &


!NjN
!_j_