Loại 1: VIẾT
PHƯƠNG TRÌNH DAO ĐỘNG:
x A t
ω ϕ
= +
CON LẮC LÒ XO
!"
K
f
T m
π
ω π
= = =
#$%
!"&
' ()*
+$,-./0123
v
A x
ω
= +
4567/28#$
9
123:(4
x A
v
ϕ
ϕ
ω ϕ
=
⇒ =
= −
L M,N2#B2+$,-2#B2+$,-OD;%$,-/O32+$,-D;(4P$12QR5,'
I;G62!2A+'5%P$2#B2+$,-Q
S M,N32T$29QR5,'I;G62!+32T$2UV*QT+D)12IW2
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(42Y'5%G,O
π
ϕ
= −
Z ()*
[\(4
"$.x V A
ω
= ⇒ =
[\N2#]I^
x A v
= ± ⇒ =
[
QY'5%;'5d"
ghV2!"#$<5VD512P$H22#!%$,-;IX5%iO2#^2#B2+$,-Q
Câu 2._-212%$,-,'5`$a
S
ω
=
#$% Q>N2#]dIe2#5V'12"-2123/S" 2Y
'5%Q2#!%$,-D;
&Q.9/S2[π " 4Q .9/S2" C. .9/SS2cπ "
?Q.9/SS2"
Câu 3._-212%$,-,'5`$a
ω
=
#$% Q(32T$29D)12ODV,-.9
"
;,$,'N2#]dIea123/
" Q@jV9"
Q
2#!%$,-P$<58J5O
%>
&Q.9L
2[π L4Q.9L
2[π (Q.9L
2[Sπ Z?Q.9L
. Z 2
π
= +
÷
"
Câu 5: _-2j2,X"OG3DE"9%$,-,'5`$2#^,>2l%;L"/2J3SgmQ@)29
/j2,X":N2#]dIe;IW2,J5,2Ya%P$<5=,>Q4X5202+$,-P$122Y2T
$
&Q.9n2cn " 4Q.9n2" (Q.9Ln2[n " ?Q.9LSn2"
Câu 6: _-212OG3DE"9G%$,-,'5;a5G!9Q12<5$N2#]dIea1
23
9/L" Qo29/12<5$N2#]OD,-.9S"E'5%<5p,>Q@jVπ
9Q
2#!%$,-P$12D;
Câu 7($%$,-,'5;U/U5G!9Q?$,-20j2OD,-:2T,X"
I$,J529IeI^,-%$,-;Ie"Q?$,-20$OI^,-Ie
"/:2T,X"I$
,J5D,-Ie;123O2#Nd"Q
22#!%$,-P$$%$,-,hQ
&.
9π2"/.
B.
. Z2[ Z"
= π
C.
. L2[ Z"
= π
D.
. Z2c "
= π
Câu 9: _-212OG3DE"9G%$,-,'5;a5G!9Q12<5$N2#]dIea1
23
9/L" Qo29/12<5$N2#]OD,-.9S"E'5%<5p,>Q@jVπ
9Q
2#!%$,-,'5;P$12D;
#$
Câu 15._-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 cm
π
π
= +
B.
"4Q.9
t
"(Q.9
L
π
−t
"?Q.9
L
π
+t
"
Câu 46:_-212%$,-,'5;G<5$N2#]dIe12O1239" ;$23A,>P$
12D;$9"
Q(+29D;D)12<5$N2#]dIe2Y'5d"P$2#B2>,-/2#!%$,-
P$12D;
A. .92"QB. .92[π"QC. .92cπ "QD. .92[
π "Q
Câu 37:_-212%$,-,'5;G<5$N2#]dIe12O1239" Q$23A,>P$12
D;$
"$.
9"
Q(+29D;D)12<5$N2#]dIe2Y'5d"P$2#B2>,-Q2#!%$,-
P$12D;
π
D. .9
π
2[
Z
π
Câu 49:_-2DWD`.%$,-,'5;a5Gb9SQ42#e2>2T,X"29S<58DWOD,-
.9
";1239
Q
S
scm
π
2#!%$,-P$DWD`.O%>2;K
A. .9
−
S
D. .9
+
LS
ππ
t
#$
001:_-212%$,-,'5;G<5$N2#]dIe12O1239" Q$23A,>P$12D;
$
"$.
9"
Q(+29D;D)12<5$N2#]dIe2Y'5d"P$2#B2>,-Q2#!%$,-P$
12D;A. .92QB. .92[n QC. .92[nQD. .92vn
005:_-212%$,-,'5;0$5 2!,-D>Ie2Qs5h,T12,,E2#
/SD;Z"Q(+32T$D)12<5$N2#]dIe2Y'5d"Q2#!%$,-P$12D;
A.
x c t cm
π
π
k k k
= + +
?>@`.u
gH3,;q
QQQk k k= + +
?>M,N'5%;P$(@@M
('5%;D`.2>(4
CB
l l l= + ∆
a
l
∆
,-8P$D`.:(4
mg
l
K
∆ =
('5%;2X5P$@M
[oD`.2#Y2l,0
"
l l l A= + ∆ −
[o@Me"$
"
l l A= −
('5%;A,>P$@M
[oD`.2#Y2l,0
$. m
l l l A= + ∆ +
π
=
Q
Q 22#!%$,-P$<58J5+32T$D)I5612w32+$,-2>(4/'5
%a.53Q
4;Q_-2<58J5G3DE"9S,E2#Y;D`.O'5%;2A^D
9L"Q
$Q !"'5%;P$D`.:(4/I2#eD`.2#^G2#Y12"
9/D`.82^""-2,>
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Q],-0P$D.Q
IQ ou<58.53%a/N2#]dIe"#qI567%$,-Q22#!%$
,-P$<58J55+32T$D;D)2812/'5%a.53Q
#$L
4;LQ"-2<58J5OG3DE"9G2#Y;D`.O,-0o9LR "Qs58J5%$,-,'5`$
aF9QS{2Y2l,0Q
$Q ]5Gb;I^,-%$,-Q
IQ ]'5%;D`.A2X5;A,>2#<52#!%$,-Q42D
9"Q
Q ]123<58J5:2T,X"";'5%;D`.D;S"Q@jV9"
Q
4;SQ"-212"
2#Y;D`.O,-0G9R "2!%$,-a5Gb
k(DWD`.e"$2!DAGu;DB,;qD;"-2>(4D`.G6INI%>Q
kaDWD`.2#Y2l,0$Ve"2#^"2l^Q
-DaDA,;qOIX520
k
F k l x= ∆ +
a'5%a.53
k
F k l x= ∆ −
a'5%aD^Q
@A,;qA,>DAGY
( )
$. "$.m K
F k l A F= ∆ + =
D)12:N2#]2jj2
@A,;qA2X5
kR5
" "
K
A l F k l A F< ∆ ⇒ = ∆ − =
kR5
"
A l F≥ ∆ ⇒ =
D)12<5$N2#]D`.G6INI%>
@A,|Vu,;qA,>
"$.
N
F k A l= − ∆
D)12:N2#]2jd2
"
9/SR D. C
_&M
9RwC
"p
9R
#$S
Câu 3_-2DWD`.2#Y2l,0%$,-aI^,-L"/5Gb/SQo3DE<58LQ
@jVn
9/9"
Q
$2#NP$DA,;qA,>2%B;<58AQZ/SZRBQ/SZRQCQSZRQDQZSZR
I2#NP$DA,;qA2X52%B;<58AQZ/SZRBQRQC./LLRQDQZSR
Câu 4:(DWD`.2#Y2l,0/D`.OG3DEG6,GXQg`I,$:N2#]dIe2!
,EGu.53%a2Y2l,0"-2,>"#q28#$O%$,-Qg`I2AHS
%$,-"j2Q(9
π
9"
Q•3,-DaDA,;qA,>;DA,;qA2X5P$D`.
G%$,-D;A. SB. LC. D.
Câu 5_-2122#Y;D`.D;"O%h#$L"Q(9"
9
π
Q
=
π
:2T,X"
t
=
/DAdV#$
5VX,-P$j2,X"O,-DaD;A. RB.
RC. RD.
N
LOẠI 3: NĂNG LƯỢNG CON LĂC:
(DWD`. (DW,
-
F%9
mv
F%9
mv
F29
α
Dạng : Tính cơ năng
Bài 1_-2DWD`.%$,-,'5`$a5Gb;I^,-&Q>N2#];2!,-Ie2
Q
Bài 2_-2DWD`.%$,-,'5`$a5Gb;I^,-&Q>N2#];2!,-j,62
Q
#$Z
Bài 3_-2DWD`.%$,-,'5`$a5Gb;I^,-&Q>N2#];2!,-jLDJ
2Q
Bài 4_-2DWD`.%$,-,'5`$a5Gb;I^,-&Qt$5€G82T$;2!
,-Ie2Q
Câu 5: _-2DWD`.OG9R "/<58OG3DE"9GQo,<5$N2#]ODV,-Z"12O1
23" Q
$]I^,-%$,-A. "Q B. S" C. L" D. L"
I],-2>N2#]ODV,-.9S"&Q/S{4Q{ (Q/S{ ?Q/S{
Câu 6#Y"-212rOG3DE"9G;"-2D`.7O,-0G9LR "Q+.D;2#B2+$
,-O2l,0/32+$,-2>N2#]dIeP$12/'5%aD^Q12,EG]2]
%$,-2A%aI^,-S"Q-•
,
;•
,
P$12GO<5$N2#]O2+$,-.
9";.
9c
"D;
Câu 10:_-2DWD`.e"$/2>N2#]dIe/j12"-2123O,-Da" %+
2Y2#BD`./2!$5/L2DW,>2A,>DJ,J52^/D),O12N2#]dIe
A. /S"Q B. L"Q C. /S"Q D. S"Q
Câu 11(DWD`.%$,-2Y$a2#!.9&ω2[ϕQ(0$5€G8
2T$Ie$5;Ieπ L2!,-P$12Ie2P$D`.Q(DW%$,-,'5
;a2J3OIe
&Q#$%Q
v
4Q#$%Q
v
(QL#$%Q
v
?Q#$%Q
v
Câu 12:_-212%$,-,'5;a2#!
/S 2[
x c
π
=
"Q1232>N2#]";2
jDJ,-D;A. /S" B. " C. /S" D. S" Q
Câu 13:12%$,-,'5;a123A,>
"$.
/O23,-O„/G<5$vÞ trÝ li ,- x
1
vËt cã123
tho¶"h
9
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c„
.
QD.
9
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[„
.
Q
Câu 14:#%$,-,'5`$P$"-2DWD`./58"G3DEP$12…2!3DJ%$
,-P$DW2#"-2,N2T$A. 2
S
DJQB. 2
S
DJQC. 8"
S
ω
ω
=
?Q
ˆ L
ω ω
=
Câu 18:(DWD`.%$,-,'5`$2Y2l,0ODE%$,-•9Q
c
{DA
,;qA,>P$D`.C
"$.
9LRQ@A,;qP$D`.G12:N2#]dIeD;C9RQ4^,-%$
,-‚D;
A. "Q B. L"Q C. S"Q D. "Q
Câu 19:_-2DWD`.,$%$,-,'5`$a2#!.9&ω2Qt$5,dVD;,q2NIX5%i
,-F
,
;2F
2
P$DW2Y2T$QRT2$2jV0$5/S,-D>Ie2
2!2J3%$,-DW‚D;
&π#$%
4Qπ#$%
(Q
π
#$%
?QLπ#$%
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
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$%dV2#Y2YH2,-2
( )
l l t
;>V$
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$
[(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
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
kR5∆ϕ9Gn.
/.
U$⇒&
_$.
9&
[&
•
kR5∆ϕ9G[n.
/.
E$⇒&
_
9|&
c&
|
⇒|&
c&
|Ž&Ž&
[&
ϕ
ϕ ϕ
−
=
−
aϕ
ŽϕŽϕ
5ϕ
Žϕ
3.R5"-2122$"$,q2T'5%$,-,'5;UU2J3.
9&
ω2[ϕ
w
.
9&
ω2[ϕ
•2!%$,-2ƒE‡D;%$,-,'5;UU2J3
.9&ω2[ϕQ
(5D^2#B•.;2#B•V⊥•.Q
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
”
,6
“
26
˜
“
5
˜
$d
“
2A.
S
ππ
+=
tx
B.
S
ππ
+=
tx
C.
S
ππ
+=
tx
D.
L S
ππ
−=
tx
÷
w D.
x a t
π
π
= −
÷
w
Câu 4.g$%$,-2;JOI^,-L";"Q4^,-%$,-2ƒEO2X12#N
A.L" B.L" C." D./S"
Câu 5.(OI3%$,-,'5;UU2J3OI^,-;$I$,J5D;&
9"w&
9Z"w
&
9L"w&
L
9";ϕ
9wϕ
9π wϕ
A.
x c t cm
π
π
= +
w B.
x t cm
π
π
= −
w C.
L L
x c t cm
π
π
= −
w D.
L L
x c t cm
π
π
= +
w
Câu 7_-2122AH,q2T$%$,-,'5`$U2Y2#!$5.
9cL
π
2;
.
9L
π
2"2#!%$,-2ƒED;
A. .
9
π
2[
Z
π
"B. .
9
π
2c
Z
π
"C. .
9
π
2c
,^
”
5
”
$5
”
$
”
5
”
2d
”
6
•
•
$
•
2#–
”
#$
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