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THẲNG NỐI 2 NGUỒN.
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HÌNH VUÔNG…
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:@3',dH)#;.e)@G.#%4,8)E:V,8
4 Sk Sb Yb Yi
Câu 8:*Ee)@G.#+f>D)#XH4.U.##+i.,?-+/:;.LH#+.6(@G.C6k. +:V
I)*Ee)@G.84,8;)#B#.#9#%)4aj. 5M:V8:@3#H'(/,.^.:W=8:@3#H'(/,
:KE+/#+=G#B#.#9#%)4,8
4 =8k =8k Yj=8YS Sk=8Sb
Câu 9: */;))#d#+/)#/+C6)*Ee)@G..6#+f>D)#XH4=8-+/:;@X.H#+=G)FCM
oaSl.U.##+b. M.:;)*<C6)*Ee)@G.=aj.\C 0=8,8#+:V)*Ee)@G.C+/.#/
4,8#B#=? 5M:V8:@3#H'(/,.^.:W=8:@3#H'(/,:KE:g+#B#.#9#%)4,8
4 S=8SS =8k Yj=8YS Sk=8Sb
Câu 10:~e)@G..6#+fC6.74=8.U.##+Y.-+/:;:<#z+.L)FCM.LH#+)#'/
H#@7=?6.=Ge)@G. VI)*E4.U.#)*:Vu,8Y.,8:VFu#A),?-+/:;
=G(E:;.^.:W *E:@3)*z)1u:@3>d#S.Ise)@G..6CM:V,?-+/:;=G(E:;.^.
:W,8
4 Yb Yk jS Y
Câu 11:*/)#d#+/)#/+C6)*Ee)@G.#+f4.U.##+Y.-+/:;@X.H#+ V
)*E4F)*:V‡.`+4#A).U.#‡,8Y.,?-+/:;.^.:W 5M:V-+/:;.^.:W)*E:@3',dH
)#;.e)@G.#%4,8)E:V,8
4 :V S:V j:V i:V
Câu 3: *Ee).#A),[.6#+fC6>D)#XHH#U)*+#+-+/:;
Y
a+./Cω)•
S
a+Cω) >#/2.U.#9+#+
f,85
Y
5
S
ajSλ [)*E:/W5
Y
5
S
.6A:V.^.:W-+/:;.LH#+=G
2
#0:UHCM:$
4 j:V i:V :V k:V
9
Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
Câu 4*Ee).#A),[.6#+f>D)#XH5
Y
5
S
-+/:;=GH#@7)*B#)@7K
Y
a+./C‰)=8
S
:VI)*E:/W‡ D)‡a.=8‡ak. 5M:VI)*E:/W.6(E:;.^.:W=8.LH#+=G‡
,8 4 i k
Câu 7:~e).#A),[.6#+fC64.U.##+Y!.-+/:;)#'/H#@7)#J:K=GH#@7)*B#,8
4
a
a+./CSπ)Q=G))d#(ICT M.:;)*<C6.`+e).#A),[,8i.\C 0,8:Vse).#A),[
F4#A)C+/.#/H#F)_.#A),[)W-+/:;=G(E:;.^.:W=8.LH#+=Gf4 #/2.U.#4,8
4 . S. i. S
S
.
CHUYÊN ĐỀ 7: VỊ TRÍ GẦN NHẤT HOẶC XA NHẤT CỦA ĐIỂM M DAO ĐỘNG VỚI BIÊN ĐỘ CỰC ĐẠI, CỰC
TIỂU NẰM TRÊN ĐƯỜNG THẲNG VUÔNG GÓC VỚI S
1
S
2
.
Câu 1QRSYST */#)@X+/)#/+C6@G.#+f-+/:;)#'/H#@7=?6.=Ge)@G.
.L(E:;.LH#+.L)FCMl:@X.:e))W#+:V5
Y
=85
S
.U.##+Y. M.:;)*<C6)*Ee)
@G.,8.\C rn).U.:V)*Ee)@G.)#;.:@3)*z)15
Y
(U>d#5
Y
5
S
e)@G.,8Y\C *Ee)@G.cn):@3)*z)14(U>d#4 V)*E:@3)*z-+/:;=G(E:;.^.
:W.U.#:@3)#Jg+4;):/WF#A),8
4 Ybk Y!k Y!! Yji
Câu 7:*Ee))#/U.#A),[)W4=8.U.##+S.@3)+(M)*d#+f
:f(;.6)FCMSl M.:;)*<C6)*Ee))#/U.#A),[=a.\C B#
=?4I)*Ee))#/U.#A),[‡,8)*:V.`+ 0:VI
)*E,8:VF‡#A)-+/:;=G(E:;.^.:W #/2.U.#)x:D‡,8
4 YS. Sb. S. j.
Câu 8: +f5
Y
5
S
.U.##+k.H#U)*+#+C6.6H#@7)*B#
Y
a
S
a+./CSw) 56C#*+)*<=G)M.:;b\C V)*Ee).#A),[
.U.#:<=8-+/:;.LH#+=G5
Y
5
S
=8F5
Y
5
S
#A).6H#@7)*B#,8
4
aS+./CQSπ)vYSπT
aS+./CQSπ)vbπT
Câu 9: #/#+fC65
Y
=85
S
.U.##+b. <;)H#d+.`+5
Y
5
S
,A)#E#+:V5
j
=85
i
C+/.#/5
j
5
i
ai.
=8#XH)#8##B#)#+.15
Y
5
S
5
j
5
i
D)(@G.C6
Ycm
λ
=
)*E)*N.u +:V=8"I)*Euc.6uai.=8u"ab. q.#.#Vfu
S
)*E)*N.u:D=q)*d
C+/.#/6.u
S
".6U)*q,G#A))#BH#F)_@G.)W>#?-+/:;.zH#F)_@G.)W"-+/:;=G(E:;
.^.:W D)9+=8">#?.z.^.:W8/>#U. *E:/Wu:VF#A)8.U.H#F)_@G.-+/:;=G
(E:;.^.:W.U.#;):/W,8
4 YY. ji. S. S.
CHUYÊN ĐỀ 8: VỊ TRÍ, SỐ ĐIỂM DAO ĐỘNG CÙNG PHA HOẶC NGƯỢC PHA VỚI 2 NGUỒN TRÊN ĐOẠN
THẲNG VUÔNG GÓC VỚI 2 NGUỒN.
Câu 1:*Ee)@G..6SfC6M#)#+4=8.U.##+;)>#/24aSi. @G.C6
λ
aS.
+:V=8)*Ee)@G..L.U.#:<)*:V.`+:/W4;):/WYk.=8.L.U.#:<SfC6
=84=8 5M:V)*E:/W-+/:;.LH#+=GSf,8
4 b k !
Câu 2 *Ee)@G..6#+f>D)#XH4.LH#+.U.##+;):/WYS.:+-+/:;=?6.=Ge)
@G.)W/*+C6=G(@G.C6Yk. 0,8;):V)*Ee)@G..U.#:<#+f=8.U.#)*:Vu.`+
:/W4;)>#/2b. [)*E:/WuCM:V-+/:;.LH#+=Gf,8
4 S j i
Câu 3*Ee)@G..6#+f>D)#XH4.LH#+.U.##+;):/WYS.:+-+/:;=?6.=Ge)
@G.)W/*+C6=G(@G.C6Yk. 0,8;):V)*Ee)@G..U.#:<#+f=8.U.#)*:Vu.`+
:/W4;)>#/2b. [)*E:/WuCM:V-+/:;@X.H#+=Gf,8
4 S j i
Câu 4*Ee)@G..6#+fC6M#+4=8.U.##+>#/24aYSQ.T:+-+/:;=?6.
=Ge)@G.)W/*+C6.6(@G.C6λaYk. =8,8#+:V>#U.#+)*Ee)@G..U.#:<#+f=8
.U.#:<)*:Vu.`+4;)>#/2b. 5M:V-+/:;.LH#+=Gfs)*E:/W,8
4 j Y k
Câu 5W#+:V4=8)*Ee)@G..U.##+;)>#/2Yk..6#+fC6>D)#XH-+/:;:<#z+=G
. Yb.
Câu 8: +fC6>D)#XH:e))W4=8.U.##+S.-+/:;)#'/H#@7)*B#a+./CQ‰)T)*Ee)@G.
./(E:;>#?:p(@G.C6λaj. 0u,8)*:V.`+4 ;):VI)*E:@3)*)*^.4-+/
:;.LH#+=G.U.f4=8.U.#4#/e.;):/W#[#A),8
4 YS. Y. Yj . Y.
Câu 9:
*Ee)@G..6#+f>D)#XH5
Y
5
S
.U.##+k
S
.-+/:;)#'/H#@7)*B#
tau
π
S./C
=
QT M.:;)*<C6)*Ee)@G.,8i\C=8(E:;C6>#?:p)*/gU)*B#)*< VF#A)-+/
:;=?H#+=G.U.fI)*E:@3)*)*^..`+5
Y
5
S
.U.#5
Y
5
S
;):/W
11
Th.s Trần Quốc Dũng -_0909959462
Y
5
S
)*Ee)@G..U.##+j.H#U)*+#+-+/:;:<#/8.LH#@7
.L)FCMoal=8H#+(+:F(I>#? D))M.:;)*<C6)*Ee).#A),[=ak\C #9:VI
)*E:@3)*)*^..`+:/W5
Y
5
S
8C6)p#XH)W:6,?-+/:;@X.H#+=GC6)p#XH)WuQu,8
)*:V.`+5
Y
5
S
T.U.#u;)>#/2#[#A),8
4
k
. k
k
. i
k
. S
k
.
Câu 3: ~e).#A),[.6#+fC64.U.##+Yk.-+/:;)#'/H#@7)#J:K=GH#@7)*B#
)./C+
4
π==
Q=G))d#(ICT M.:;)*<C6se).#A),[,8.\C 0u,8)*:V.`+4
:Vse).#A),[I)*E:@3)*)*^..`+4=8Fu#A)C+/.#/H#F)_.#A),[)W-+/:;@X.
4
a+./CQYπ)T•
a(./CQYπ)T
M.:;)*<C6)*Ee).#A),[Y\C ‡,8)*:V.`+4 ,8:VI)*E:/W4‡,8:VI)*E
:/W‡ D)‡a.=8‡ak. 5M:VI)*E:/W.6(E:;.^.:W=8.LH#+=G‡,8
4 i k
Câu 7: +:V4)*Ee)@G.,8(+:P#.`+)++.:<.6.W#S.)*/:64=8,8#+fH#U)C6
.6H#@7)*B#
TTQS./CQS
SY
cmtuu
π
==
C6)*<)*Ee)@G.>#?C2=8.6=%)M.SQ.\CT )*
:V.`+4 5M:V-+/:;@X.H#+=G:V)*E:/W,8
4 i k j
Câu 8: +:V4)*Ee)@G.,8(+:P#.`+)++.:<.6.W#Yk.)*/:64=8,8#+fH#U)C6
.6H#@7)*B#
TTQS./CQS
SY
cmtuu
π
==
C6)*<)*Ee)@G.>#?C2=8.6=%)M.SQ.\CT
)*:V.`+4 5M:V-+/:;.LH#+=G:V)*E:/W,8
4 i S j
CHUYÊN ĐỀ 10: VỊ TRÍ, SỐ ĐIỂM DAO ĐỘNG VỚI BIÊN ĐỘ BẤT KÌ.
Câu 1: *Ee)@G.)W#+:V5
Y
a
i./CQi
w
)
TQ
4
=8
)d#(I))d#(ICT D))M.:;
)*<C6)*Ee).#A),[,8j.\C [)*E:@3+*+(/,.6:P#‡I)*E:@3)*)*^..`+4
.U.#u;):/WY.=8:g+4.6(+/#E:V-+/:;=G(E:;(IQu,8)*:V.`+
4T
4 Yj S Sk Sb
12
Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
Câu 3: *Ee)@G.)W#+:V5
Y
5
S
.U.##+b.@3)+:e)#+fC6.7>D)#XH-+/:;:<#/8)#'/
H#@7)#J:K=GH#@7)*B#
4
ak./Ciπ)=8
ab./CQiπ)TQ
4
=8
•I.U.#‡;):/Wj.C{-+/:;
=G(E:;
4 Y S
Câu 5: *Ee)@G..6#+fH#U)C6>D)#XH4.6.L(E:;+aSQ.T.L)FCMoaSQlT@X.H#+
#+ /(E:;C6>#?:p=%)M.C6=abQ.\CT E:;-+/:;)p#XH)W:V.64aYSQ.T
aYQ.T,8
4 iQ.T SQ.T
22
Q.T
Câu 6: +fC6>D)#XH,?@X.H#+.6.L(E:;41*+)WC^+/)#/+=G(E:;S4 D)t)F
CM-+/:;.`+#+f,ES,F)#B(E:;-+/:;)W>#8,8
4 4 4
S
S4
Câu 7: +fC6>D)#XH4=8.L)FCM.L(E:;=8.LH#+ /(E:;C6>#?:p V
4)#'/)#K)^)#J#8(D)}4a4v D(E:;-+/:;)p#XH)W.6U)*q,8k)#B
(E:;-+/:;)p#XH)W.6U)*q
4 #@+:`-9> j k
j j
.
Câu 8: +C6@G.:@X.)W/(s.U.f4.6(@G.C6#@#+=8(Ib €C6*E()1*+)W
.U.#4;):/W-
Y
aj=8.U.#;):/W-
S
a-+/:;=G(E:;(I4 D-+/:;)W.U.f@X.
H#+#+)#B(E:;-+/:;)W-/.2#+f1*+,8
4 4 S4 j4
Câu 9: +fC6>D)#XH4)*Ee))#/U.#A),[-+/:;)#'/H#@7)*B#
i /CQY T
−
j mm
−
j j mm−
Câu 10: ~e))#/U.`+;).#A),[.6#+f>D)#XH4.U.##+Y.-+/:;)#'/H#@7)#J:K
=GH#@7)*B#,F,@X),8
4
aj./CQiw)|w\kT.•
ai./CQiw)|Sw\jT. #/(D))M.:;)*<C6,8i.\C
;):@3)*z.6)1,8)*:V.`+4I)*Ee)@G..6(U>d#ai. 5M:V-+/:;=G(E:;
..6)*E:@3)*z,8
4 j jS ji jk
Câu 11: *E e)@G. .6 #+ f 4 -+/:; ,F ,@X))#'/ H#@7 )*B#
Q TQ T
S
A
U a cos t cm
π
ω
= +
=8
Q TQ T
B
U a cos t cm
ω π
= +
/=%)M.=8(E:;C6>#?:p)*/gU)*B#)*<C6 U.:V)#;.e)@G.
j
i
π
Câu 13:~(<e);).#A),[.6#+fH#U)C6>D)#XH5
Y
=85
S
.U.##+S. +f8-+/:;)#'/
H#@7)#J:K.6H#@7)*B#,F,@X),8
Y
a./Ciπ)QT=8
S
a./CQiπ)|πTQT M.:;)*<C6)*E
e).#A),[,8b.\C rn).U.:V)*E5
Y
5
S
0‡,8)*:V.`+5
Y
5
S
•I.U.#‡;):/Wj.C{-+/:;
=G(E:;
4 Y S
Câu 14:~e))#/U.#A),[.6Sf>D)#XH4.U.##+Y.-+/:;)#'/H#@7)#J:K.6H#@7
)*B#,F,@X),8
A
aj./CQi
π
Câu 5: #J:q#8/C+:1,8sai
4 M=GC6-x>#/2.U.#9+S(N#/e.S$),E)DH(I;)_+(@G.C6
*/+/)#/+C6(E:;C6)p#XH.^.:W>#:;,.#H#+(ICM.#•π
*/+/)#/+C6(E:;C6)p#XH.^.)V>#:;,.#H#+(ICM,•_+π
5^)*<C6,8C^)*<t,@X=8t,@XH#N)#;.(E:;-+/:;C6
Câu 6: #J:q#8/C+:1,8sai
4 +/)#/+,8C^)p#XH.`+S#+#<C6
56-x,8C6)p#XH.`+C6)G=8C6H#2cW)*E.LH#@7)*<
GC6-x.U.$),8#9:V.M:q#
U.C6>D)#XH,8.U.C6.6.LH#@7.L)FCM#CMH#+>#?)#+:p)#'/)#3+
Câu 7;)C6-xc2*+)*ECX-1#+:F.M:q#=G)FCMo D)t)FCM,ESo)#B
4 Ž.6C6-x.U.$)C6(+:F)*s)#8#(NC6
Ž.6C6-x.U.(NC6(+:F)*s)#8#$)C6
#?.6C6-x9+
Ž.6C6-x.U.(NC6(+:F,$.8=Ž,8(NC6
Câu 8:*E;)CX-1-8S:+.6C6-x=G)FCMl@3)+)#A/8#+:F-1.M:q#.z.6j
:V>#U.,?:KE %)M.)*<C6)*E-1,8
4 i\C \C b\C k\C
Câu 9:;)-14-8Yb.t)#JI+:F.M:q#:F4]=8/;)(2*)FCMYl #(2
*#/W):;@3)+)#A)*E-1.6C6-xfk(6C6=G4c'#@;)$) d#(@G.C6=8=%)M.
)*<C6)*E-14
4 λaj•=ak\C λak•=ak\C λaj•=aj\C λak•=aYS\C
Câu 10:*E-14-8S.6C6-x.6#+(NC6:F4M=Gf-+/:;Q./,8;)$)C6T:F
.M:q# B)FCM-+/:;.`+f(D)=%)M.C6)*E-1,8S\C
4 Sl Sl l Yl
Câu 11:;)-1:8#f4-8k..6:F.M:q#:F4].=8/;)#U#1)#/+:+-+/:;=G)FCM
oal #1)#/+*)*E-1.6C6-x=Gj(NC6 %)M.)*<C6)*E-1,8
4 =aY\C =aSb\C =aS\C =aS\C
Câu 12*ECX-1u4:F4.M:q#=8:Fu-+/:;:<#/8=G)FCMSl)#B)*E-1.6$) M)*E-1
*)#8#S(NC6)#BsuH#2-+/:;=G)FCM
λ
ajk.•vaS\C
λ
ajk.•vaS.\C
λ
ajk.•vaS.\C
λ
ajk.•vaS\C
Câu 21: ;)+:.6-z:c/+.#<)FCMl:g+ e)+.#1:H#d+)*E;)-1)#nH4.t
+=G#+:F.M:q#.#<-8CX-1k. +)#A)*E-1.6C6-x=GS(6C6 d#=%)M.C6)*<
)*E-1Z
4 k\C k.\C k\C k.\C
Câu 22: ;)CX-12#-8S.:F)^-/=8:F4-+/:;=G)FCMo M.:;)*<C6)*E-1,8
i.\C <>=<)FCM:Vc2*+#)@XC6-x)*E-1,8
4 oaYkQ>|Y\ST oabQ>|Y\ST oab> oaYk>
Câu 23: ;)MCU/#s#+:F)W/*+C6-x.#/1=Gj$) #/2.U.#9+S$),E)DH,8S. #<-8
.`+MCU/,8
4 b. k. YS. j.
Câu 24: ;)CX-1:8#f-8.6;):F)^-/:F>+M=G;)#U#1)#/+*=G)FCMbl %
)M.)*<C6)*E-1,8jS\C )*E-1.6C6-x d#CM(6C6E#B#)#8#)*E-1
4 k j i
Câu 25: 14a!..6:F4.M:q#:F)^-/ #)FCM)*E-1,8Yl)#B)*E-1.6b$)C6-x
+Td#>#/2.U.#)x4:D$))#K4 S bi Ykb b
(TD.M:q#=8)M.:;)*<C6>#?:p8M.6C6-x)*E-1)#BH#2)#+:p)FCMo;),@X
#[#A)(I(+/#EZ 4 Y\jl bl kl Yjjl
CHUYÊN ĐỀ 2: PHƯƠNG TRÌNH SÓNG DỪNG.
Câu 1: V)#K.C6)p#XH.`+C6)G=8C6H#2cW)W;):V.U.#:F.M:q#>#/2c.#/(s
( )
2cos .sin 20
4 2
4 . S. S
Câu 4: *E-1:8#f.6C6-xc2*+ #@7)*B#:;-3.`+-1)#'/)0+:;c=8)#3+).#/(s
5cos 0,05 .cos 8
2 2
u x t
π π
π π
= + −
÷ ÷
)*/:6c)d#(I.=8))d#(IC M.:;)*<C6)*E-1,8
4 S.\C Yk\C Y\C i\C
15
Th.s Trần Quốc Dũng -_0909959462
CÔNG DUY - !" #$#%
&'()*)+,)-#./- ./ Tài Liệu LTĐH
Câu 5;)C6-x)*E-1.6-W
S./CQ T./CQS T
i S S
d
u t mm
π π π
π
= + −
)*/:6,8,:;)W)#3:V).`+
H#F)_)*E-1.U.#:F.M:q#.`+-1;)>#/2,8-Q.T %)M.)*<C6)*E-1,8
4 b.\C Y.\C k.\C i.\C
Câu 6: *E:/W-1:8#f4.6C6-xc2*+ V)#K.C6)p#XH.`+C6)G=8C6H#2cW)W;)
:V.U.#:FH#2cW;)>#/2c.#/(s
π π
=
Q.T)*/
:6c)d#(I=8))d#(IC B=%)M.-+/:;.`+H#F)_)*E-1QcaS.T=8/,$.)aY\iC,8
4 vjYi.\C kSb.\C Si.\C vYi.\C
Câu 9: ;)C6-x)*E;)CX-1.6-WaiCQS
π
cT./CQ
ω
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