1
75l1*Ô,+é&+ễ1*9lj1*
KHOA TON - &é1*1*+ấ
%ẩ2&ẩ2
7ơ,1*+,ầ1&ỡ8.+2$+é&6,1+9,ầ1
.+$,7+ẩ&7ậ1+11*&ờ$0ẩ<7ậ1+&$6,2
FX-(67521**,Ư,0ĩ76ễ%ơ,73&+lj1*
'$2ĩ1*&j9ơ'ẹ1*,ấ1;2$<&+,8
TH8ĩ& CHlj1*75ẻ1+97/ộ
�3�+����7�+���- 2014
23
KLầQWKẽXM
9tGộFKRRƠQPƠFK$0FKớD5&PFQếLWLSYòLRƠQ0%FKớDTXQFĐP
L,r . Tỡm ABU ?
�%�L��W����100 2 os(100 )
3AMu c t
�S
�S� � �
100 2 os(100 )
6MBu c t
�S
�S� � �
�&�i�F�K���J�L�+�L��
�3�K�ñ�ï�Q�J���S�K�i�S���W�U�X�\�I�Q���W�K�Y�Q�J �3�K�đ�ï�Q�J�� �S�K�i�S�� �V�u�� �G�m�Q�J��
máy tính
Ta có : AM AM MBU U U� � �
Suyra: 2 2 2
0 2 os( )
3 6AB AM MB AM MBu u u u u c
� S � S
� �� �� �� ��
2 2
0
2 2
2 os( )
3 6
(100 2) (100 2) 2.100 2.100 2 os( )
3 6
AB AM MB AM MBu u u u u c
c
� S � S
� S � S
� �� �� �� ��
� �� �� �� ��
= 200(V)
t 1
1
2
2
.sin .sin
an
. os . os
AM
AM MB
MB
u u
u c u c
� M � M
�M
� M � M
��
�
��
=
100 2.sin 100 2.
3 6
100 2. os 100 2. os
3 6
Sin
c c
� S � S
� S � S
��
��
��
��
suy ra
12
�S
�M
��
�
�9�±�\�� 200 os(100 )
12ABu c t
�S
�S� � �
�&�i�F���E�m��F��
6ủGộQJSKtP
ầ PjQ KuQK [XâW
KLậQ&03/;
%âP
ầFjLằWGƠQJWẹDí
FừF )
���%�©�P 4
�F�K�Đ�Q�� �ÿ�k�Q�� �Y�Ï�� �ÿ�R�� �O�j��
Radian(R)
Ta có:
1 2AM MB ABu u u�M �M �M�‘ �� �‘ � �‘
���1�K�±�S���J�L�i���W�U�Ï��
AMU SHIFT ( )�� 1�M ��
MBU SHIFT ( )�� 2�Mhay
100 2 SHIFT ( )��
3
�S
�� ��
100 2 SHIFT ( )��
6
�S
=
24
200
12
�S��
�‘
�9�±�\
200 os(100 )
12ABu c t
�S
�S� � �
x 6RViQKWKỏLJLDQOjPEjLWKHRSKmkQJSKiS
JLĐLWUX\QWKếQJSK~WV
JLĐLEàQJPi\WtQKV
1K5Q[pW YòLEjLWRiQFíQJLậQiSVủGộQJPi\WtQKFKRNWTXĐQKDQKKkQUâW
QKLXVRYòLJLĐLEàQJSKmkQJSKiSWUX\QWKếQJJL~SWLWNLậPWKỏLJLDQWURQJFiFEjL
WSWUFQJKLậP
%jLWRiQKíSHQ
&KRKíSHQNtQFKFKớDWURQJSKôQWủ5/&PFQếLWLSằWYjRôX
RƠQ PƠFK LậQ iS [RD\ FKLX 0 os( )u U c t� Z � M� � �, 0 os( )i I c t� Z � M� � ��ÿ�R�¥�Q�� PƠFK FKớD
QKúQJSKôQWủQjRJLiWUẽFởDFiFƠLOmỗQJy
&iFKJL+L
3KủùQJSKiSJL+LWUX\IQWKYQJ 3KủùQJSKiSJL+LE9QJ mỏy tớnh
7uPWQJWUó=0
0
U
Z
I
7tQKJyFOậFKJLúDXôXPƠFK
và i: tan u i�M �M �M� � �
L CZ Z
R
��
suy ra
tan 0�M� ! � Ÿ�ÿ�R�¥�Q���P�¥�F�K���F�K�í�D���5�/
tan 0�M� � � Ÿ�ÿ�R�¥�Q���P�¥�F�K���F�K�í�D���5�&
tan�M� �f RƠQPƠFKFKớD/&
&iFEmòF
6ủ GộQJSKtPầPjQ KuQK[XâW
KLậQ&03/;
%âP 1 ầ ầ
FKX\ầQYGƠQJcỏc a+bi
%âP �F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j��
�ÿ�Ý���'��
+Ta có
u
z
i
� = 0
0
u
i
u
I
�M
�M
�‘
�‘
���Q�K�±�S���J�L�i���W�U�Ï��
25
���7�t�Q�K�� �J�L�i�� �W�U�Ï�� �ÿ�¥�L�� OmỗQJ Wù ELầX
WKớF
Z = 2 2( )L CR Z Z� � � �
tan L CZ Z
R
�M
��
�
0U ( )�� u�M �y
0
I
( )�� i�M� �K�L�Ç�Q���W�K�Ï�������D���E�L�����K�R�»�F���D-bi, bi , -bi
Ta có ( )L CZ R Z Z i� �� ��
a+bi suy ra a = R, b = LZ �ÿ�R�¥�Q���P�¥�F�K���F�K�í�D��
RL
a-bi suy ra a = R, b =CZ �ÿ�R�¥�Q�� �P�¥�F�K�� �F�K�í�D��
RC
bi, -�E�L���ÿ�R�¥�Q���P�¥�F�K���F�K�í�D���/�&
9tGộ PíWKíSNtQFKFKớDWURQJSKôQWủ5/&PFQếLWLSQXằWYjR
ôXPƠFK LậSiS[RD\FKLX100 2 os(100 )
4
u c t
S
S � ���9�����W�K�u���F�m�á�Q�J���ÿ�Ý���G�z�Q�J���ÿ�L�Ë�Q���ÿ�L��
�T�X�D�� �K�Ý�S�� �ÿ�H�Q�� �O�j����2 os(120 )( )i c t AS RƠQ PƠFK FKớD QKúQJ SKôQ Wủ QjR JLi �W�U�Ï�� �F�ë�D��
�Q�K�ó�Q�J���S�K�«�Q���W�đ���ÿ�y�"
�&�i�F�K���J�L�+�L��
�3�K�đ�ï�Q�J���S�K�i�S���W�U�X�\�I�Q���W�K�Y�Q�J �3�K�đ�ï�Q�J���S�K�i�S���J�L�+�L���E�9�Q�J máy tính
0
0
100 2
50 2( )
2
tan( ) 1
4u i
u U
Z
i I
Tan
�S
�M �M �M
� � � � �:
��
� �� � � ��
���R�¥�Q���P�¥�F�K���F�K�í�D���5�&
Ta có: Z = 2 2
CR Z��
1CZ
Tan
R
�M
��
� � ��
Suy ra: R = 50 (�: )
ZC= 50(�: )
�&�i�F���E�m��F��
6ủ GộQJ phớm ầPjQ KuQK[XâW
KLậQ&03/;
%âP 1 ầ ầ
FKX\ầQYGƠQJFiFDEL
%âP �F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j��
�ÿ�Ý���'��
+Ta có
u
Z
i
� = 0
0
u
i
u
I
�M
�M
�‘
�‘
=
100 2 45
2 0
� ‘ � �
�‘
�����Q�K�±�S���J�L�i���W�U�Ï��
100 2 SHIFT ( )�� -45 : 2
26
SHIFT ( )�� 0 = 50-50i
�9�±�\�����R�¥�Q���P�¥�F�K���F�K�í�D���5�&
R = 50(�: ), ZC = 50(�: )
�x �6�R���V�i�Q�K���W�K�á�L���J�L�D�Q���O�j�P���E�j�L���W�K�H�R�������S�K�m�k�Q�J���S�K�i�S��
���J�L�§�L���W�U�X�\�Å�Q���W�K�Õ�Q�J���������S�K�~�W�������V
JLĐLEàQJPi\WtQKV
1K5Q[pW GƠQJEjLWRiQKíSHQOjGƠQJEjLNKyWX\QKLrQYòLSKmkQJSKiSVủGộQJ
Pi\WtQKFKRUDNWTXĐQKDQKFKyQJPjNK{QJPâWQKLXF{QJWtQK WRiQYjELậQOXQ
7uPKậVếF{QJVXâWWURQJPƠFKLậQ[RD\FKLX
3KủùQJSKiSJL+LWUX\IQWKYQJ 3KủùQJSKiSVuGmQJPi\WtQK
6ủGộQJYjELQLFiFF{QJWKớF
+ậVếF{QJVXâWWURQJRƠQPƠFK
RLC: os
R
c
Z
�M� Hay os Ru
c
u
�M�
RrLC: os
R r
c
z
�M
��
�
hay cos R ru u
u
�M
��
�
�7��Q�J���W�U�������=��� ��2 2( )L CR Z Z� � � �
tan L CZ Z
R
�M
��
�
Suy ra cos �M
���6�ñ�� �G�é�Q�J�� SKtP ầ PjQ KuQK
[XâWKLậQ&03/;
%âm 1 ầầ
FKX\ầQYGƠQJFiFDEL
%âP FKẹQkQYẽ
ROjí'
( )L CZ R Z Z i� �� ��
u
Z
i
�
Tính cos�M �Q�K�á���P�i�\���W�t�Q�K��
Z Z �M� � ‘
9tGộ: CKRRƠQPƠFK$%JìP$0Yj0%PFQếLWLSRƠQ$0JìPLậQWUó
WKXôQ5 : YjTXQFĐPWKXôQ/ 1
S
+RƠQ0%OjWộLậQFyLậQGXQJF
ELầXWKớFLậQiSWUrQPƠFK$%Yj0%OôQOmỗWOj
27
100 2 cos(100 )( )
4AMU t V
�S
�S� � � và 200cos(100 )( )
2MBU t V
�S
�S� KậVếF{QJVXâWWUrQ
RƠQPƠFK$%Oj
A.
3
os
2
c �M� B.
2
os
2
c �M�
C. os 0,5c �M� D. os 0,75c �M�
Bài gi�+i:
�3�K�đ�ï�Q�J���S�K�i�S���J�L�+�L���W�U�X�\�I�Q���W�K�Y�Q�J �3�K�đ�ï�Q�J���S�K�i�S���V�u���G�m�Q�J���P�i�\���W�t�Q�K
Ta có 100LZ � � :
100 2AMZ � � :
I =
100 2
2100 2
AM
AM
U
Z
� � (A)
2.100 2
200( )
2
MB
C
U
Z
I
� � � �:
Z= 2 2( )L CR Z Z� � � �=
100 2( )�:
100 2
os
2100 2
R
c
Z
�M� � �
���i�S���i�Q���%
Ta có : AMZ =(100+100i)
�W�Ù�Q�J�� �W�U�ã�� �S�K�í�F�� �F�ë�D�� �ÿ�R�¥�Q�� �P�¥�F�K�� �$�%�� �O�j����
( )
.
(1 ).
AB AM MB
AB AM
AM
MB
AM
AM
U U U
Z Z
i U
U
Z
U
��
� �
�
6ủ GộQJ SKtP ầ PjQ KuQK [XâW
KLậQ&03/;
%âP 1 ầầFKX\ầQ
YGƠQJFiFDEL
%âP �F�K�Ñ�Q�� �ÿ�k�Q�� �Y�Ï�� �ÿ�R�� �O�j��
�ÿ�Ý���'��
(1+
80 0
100 90
�‘
�‘
) �u(100+100i)= 141.42 45� ‘ � �
�%�©�P��SHIFT 2 1 = - 45
�%�©�P��cos(ans) = �0�j�Q���K�u�Q�K���K�L�Ç�Q���W�K�Ï��
2
2
�x �6�R���V�i�Q�K���W�K�á�L���J�L�D�Q���O�j�P���E�j�L���W�K�H�R�������S�K�m�k�Q�J���S�K�i�S��
���J�L�§�L���W�U�X�\�Å�Q���W�K�Õ�Q�J���������S�K�~�W�������V
JLĐLEàQJPi\WtQKSK~WV
28
*) /mXờ 9LậFVRViQKWKỏLJLDQóFiFSKôQWUrQmỗFWKừFKLậQEóLQKyPQJKLrQFớX
WjLOjNWTXĐWUXQJEuQKFởDOôQWKừFKLậQ
iQKJLiFKXQJ
- 9LậFVủGộQJPi\WtQK&$6,2);(6WURQJJLĐLFiFEjLWSYWOtmQrXFy
QKLXmXLầPQKm
7URQJJLĐLWRiQEàQJSKmkQJSKiSWUX\QWKếQJWDFyVủGộQJPi\WtQKQKmQJ
y FK Oj ếL YòL YLậF WKừF KLậQ FiF WtQK WRiQ Fk EĐQ &zQ ếL YòL JLĐL EjL WRiQ YW Ot
EàQJSKmkQJSKiSVủGộQJPi\WtQK&$6,2);(6WDJLĐLEjLWRiQPíWFiFKEjLEĐQ
WKHROSWUuQKmFyVạQJL~SNK{QJFKYLậFJLĐLEjLWRiQyPjFzQJL~SFKRYLậFSKiW
WULầQầJLĐLFiFEjLWSFãQJGƠQJóPớFíFDRKkQ
mDUDNWTXĐQKDQKFKyQJWLậQOỗL
*L~SWLWNLậPWKỏLJLDQF{QJVớF
/jSKmkQJSKiSWếLmXQKâWWURQJJLĐLEjLWSWQJKỗSWùEDEếQ �G�D�R���ÿ�Ý�Q�J���F�k����
�ÿ�L�Ë�Q���W�U�ã���O�r�Q
- �7�X�\�� �Q�K�L�r�Q���� �Y�L�Ë�F�� �V�ñ�� �G�é�Q�J�� �P�i�\�� �W�t�Q�K�� �&�$�6�,�2�� );(6 FấQJ FzQ QKLX KƠQ FK
QKm
.KLQKẹFVLQKOmỏLELQJWURQJELQLF{QJWKớFGQQSKộWKXíFYjRPi\
WtQKQKLXF{QJWKớFkQJLĐLFấQJSKDVủGộQJPi\WtQK
+ Mỏy tớnh l F{QJFộPi\PyFQrQWURQJQKLXWUmỏQJKỗSVWUóQrQFớQJQKF
0íWVếOmXờ
.KLVủGộQJPi\WtQKWURQJWtQKWRiQKẹFVLQKVLQKYLrQYjJLiRYLrQFôQOmXờ
1rQFKẹQkQYẽJyFOjíKRằF5DGGƠQJKLầQWKẽOjWẹDíFừFKD\HFDFVDRFKR
phự KỗSYòLEjLWUiQKQKôPOQ
1rQVủGộQJSKpSFKLDSKkQVếWKD\FKRSKpSFKLDWKmỏQJầWUiQKQKôPOQQXVủ
GộQJSKpSFKLDWKmỏQJWKuQrQVủGộQJNqPGâXQJRằFkQWURQJFiFELầXWKớF
/mXờFKẹQOƠLFKíWtQKEuQKWKmỏQJNKLWUóYFKíWtQKFkEĐQ
1JRjLYLậFVủGộQJPi\WtQK&$6,2);(6ầJLĐLEjLWSYWOtWDFấQJFyWKầVủ
GộQJ �F�i�F�� �P�i�\�� �W�t�Q�K�� �F�y�� �O�±�S�� �W�U�u�Q�K�� �W�m�k�Q�J�� �W�õ�� �Q�K�m�� �&�$�6�,�2�� );(6 &$6,2 );(6
3/86ô
29
&+lj1*0ĩ76ễ%ơ,7391'ố1*
%jLWSFKmkQJGDRíQJFk
3.1.1. 7QJKỗSGDRíQJLXKzD
D&iFEjLW5SP3X
%jL76+&K\ầQíQJFởDPíWYWOjWQJKỗSFởDKDLGDRíQJ
LXKzDFãQJSKmkQJKDLGDRíQJQj\FySKmkQJWUuQKOôQOmỗWOj1x =3cos(10t)
(cm) v 2x =4sin(10t+
2
S
FP*LDWếFFởDYWFyíOòQFừFƠLOj
A: 0,7 m/ 2s B:7 m/ 2s C:1 m/ 2s D:5m/ 2s
�%�j�L���J�L�+�L��
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2
�x SHIFT MODE 4
�x �1�K�±�S��3 0 4
2
�S
�‘ �� �‘ �©�Q��������SHIFT (-) 0 + 4 SHIFT (-)
2
�S
=
�0�j�Q���K�u�Q�K���K�L��Q���������L
�x �%�©�P��SHIFT 2 3 = [XâWKLậQ5 0.93
9\JLDWếFFừF ƠLaxma =A. 2Z =5. 210 =500 cm/ 2s =5 m/ 2s
�&�K�Ñ�Q���ÿ�i�S���i�Q���'
�%�j�L�� ������ ���7�6���+�� ������������ �&�K�X�\�Ç�Q�� �ÿ�Ý�Q�J�� �F�ë�D�� �P�Ý�W�� �Y�±�W�� Oj WQJ KỗS FởD KDL GDR
íQJ LXKzD FãQJ SKmkQJ KDL GDR íQJ Qj\ Fy SKmkQJ WUuQK OôQ OmỗW Oj
1 4cos(10 )
4
x t
�S
� � � (cm) , 2
3
3cos(10 )
4
x t
�S
� � � ���F�P���� �����Ý�� �O�ß�Q�� �F�ë�D�� �Y�±�W�� �ã�� �Y�Ï�� �W�U�t�� �F�k�Q��
�E�µ�Q�J���O�j��
A:10 cm/s B:80 cm/s C:50 cm/s D:100 cm/s
Bài g�L�+�L:
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2
�x SHIFT MODE 4
30
�x ���Ç���Q�K�±�S��
3
4 3
4 4
� S � S
�‘ �� �‘ �� �©�Q������SHIFT (-)
4
�S
+ 3 SHIFT (-) -
3
4
�S
�0�j�Q���K�u�Q�K���K�L��Q��
2 2
2 2
i
x ăQSHIFT 2 3 = [XâWKLậQ1
4
S
�o A= 1 cm
�9�±�\�� axmv = A.Z = 1.10 =10 cm/s
&KẹQiSiQ$
E&iFEjLW5SY5QGmQJ
%jL76+ +DLGDRíQJLXKzDFãQJSKmkQJFãQJWôQVếFy
ELrQíOôQOmỗWOjFPFPOậFKSKDQKDXS'DRíQJWQJKỗSFyELrQí
OôQOmỗWOj
A:1,5 cm B:7,5 cm C:5 cm D:10,5 cm
%jL76+$-2013): +DLGDRíQJLXKzDFãQJSKmkQJFãQJWôQVế
FyELrQíOôQOmỗWOjFP FPOậFKSKDQKDX
2
S
'DRíQJWQJKỗSFyELrQ
íOj
A:11cm B:17cm C:7cm D:23cm
Bi 5: 3KmkQJ WUuQK WQJ KỗS FởD KDL GDR íQJ LX KzD Fy SKmkQJ WUuQh
OôQOmỗWOj1 4 3 os( )
3
x c t
�S
�S� � � (cm); 2
5
4cos( )
6
x t
�S
�S� � � (cm)
A: x=2cos (
2
t
�S
�S �� ) (cm) B: x=2cos( )
2
t
�S
�S �� (cm)
C: x=8cos( )
2
t
�S
�S �� (cm) D: x=8cos(
2
t
�S
�S �� ) (cm)
���������������9�L�Ã�W���S�K�m�k�Q�J���W�U�u�Q�K���G�D�R���K�z�D���ÿ�Ý�Q�J���ÿ�L�Å�X���K�z�D
D&iFEjLW5SP3X
Bi 1: 9WQằQJWURQJFRQOFOz[RGDRíQJLXKzDYòLZ=10 5 rad/s.
&KẹQJyFWẹDíWUãQJYòLYẽWUtFkQEàQJFởDYW%LWUàQJWƠLWKỏLLầPEDQôX
YWLTXDOLí[ FP3KmkQJWUuQKGDRíQJFởDYWOj
31
A: x=4cos(10 5 )
3
t
�S
�� (cm) B: x=2 2 os(10 5 )
3
c t
�S
�� (cm)
C: x=4 2cos(10 5 )
3
t
�S
�� (cm) D: x=5sin(10 5
2
t
�S
�� ) (cm)
�%�j�L���J�L�+�L����
�7�¥�L���W� ���o
2
20 15
2 3
10 5
o
o
x
v
�Z
� ư
đ
x 1KS-2 3i âQ- 2 3 SHIFT ENG =
�x SHIFT 2 3 = �[�X�©�W���K�L�Ë�Q����
3
�S
� ‘ � �
�9�±�\���[� FRV5 )
3
t
S
(cm)
&KẹQiSiQ$
Bi 2: 0íWYWQKểGDRíQJLXKzDGẹFWKHRWUộF2[YòLELrQíFP
FKXNuV7ƠLWKỏLLầPW YWLTXDYẽWUt FkQEàQJ2WKHRFKLXkP3KmkQJ
WUuQKGDRíQJFởDYWOj
A: x=12cos(�St+
2
�S
) (cm) B: x=12cos(
2
t
�S
�S �� ) (cm)
C: x=12cos(
3
t
�S
�S �� ) (cm) D: x=12cos(
3
t
�S
�S �� ) (cm)
�%�j�L���J�L�+�L����
Ta có:
2
T
�S
� Z � S� � (rad/s)
�7�¥�L���W� YWTXDYẽWUtFkQEàQJ12v A Z So
7ƠLW
0
12
o
o
x
v
Z
�
�°
�o �®
� � � �°�¯
�x �1�K�±�S�����������L���©�Q������+ 12 SHIFT ENG =
�x SHIFT 2 3 = �[�X�©�W���K�L�Ë�Q������
2
�S
�‘
32
�9�±�\���[� �����F�R�V���St+
2
�S
) (cm)
�&�K�Ñ�Q���ÿ�i�S���i�Q���$
�E�����&�i�F���E�j�L���W�5�S���Y�5�Q���G�m�Q�J��
Bài 3: (76+): 0íWFKâWLầPGDRíQJLXKzDWUrQWUộF2[7URQJ
WKỏLJLDQVFKâWLầPWKừFKLậQmỗFGDRíQJWKjQKSKôQ*ếFWKỏLJLDQ
OjO~FFKâWLầPLTXDYẽWUtFyOLíFPWKHRFKLXkPYòLWếFíOj3cm/s.
3KmkQJWUuQKGDRíQJFởDFKâWLầP
A: x=4cos(20
6
t
S
) (cm) B: x=4cos(20t+
6
�S
) (cm)
C:x=4cos(20t+
3
�S
) (cm) D: x=4cos(20t-
3
�S
) (cm)
�%�j�L���J�L�+�L��
Ta có T=
3,14
100
=0,314 s =20 rad/s
�7�¥�L���W� ��
2
40 3
2 3
20
o
o
x
v
�Z
� �
�°
�o �®
�� � � �°
�¯
�x �1�K�±�S��2 + 2 3 SHIFT ENG =
�x SHIFT 2 3 = �[�X�©�W���K�L�Ë�Q����
3
�S
�‘
�9�±�\��x=4cos(20t+
3
�S
) (cm)
�&�K�Đ�Q���ÿ�i�S���i�Q���&
Bài 3: �0�Ý�W���Y�±�W���G�D�R���ÿ�Ý�Q�J���ÿ�L�Å�X���K�z�D���Y�ß�L���F�K�X���N�u�����V�����O�~�F���W� �����Y�±�W���ÿ�L���T�X�D���O�L���ÿ�Ý���[� ��-
2 2 �F�P���Y�ß�L���Y�±�Q���W�Õ�F���Y� ��-4 2�S�F�P���V�����3�K�m�k�Q�J���W�U�u�Q�K���G�D�R���ÿ�Ý�Q�J���F�ë�D���Y�±�W���O�j��
A: x=4cos(2
4
t
�S
�S �� ) (cm) B: x=10cos(2
4
t
�S
�S �� ) (cm)
C: x=4cos(
3
2
4
t
�S
�S �� ) (cm) D: x=10cos(2
3
4
t
�S
�S �� ) (cm)
33
Bi 4: 0íWYWPYjRPíWOz[RQKẵGDRíQJLXKzDYòLFKXNuV1JmỏL
WDNpRPNKểLYẽWUtFPWKHRFKLXGmkQJJếFWKỏLJLDQOjO~FEX{QJYW3KmkQJ
WUuQKGDRíQJFởDYWOj
A: x=3cos(2 tS ) (cm) B: x=3cos(2 t� S � S�� ) (cm)
C: x=3cos(2
2
t
�S
�S �� ) (cm) D: x=3cos(2
2
t
�S
�S �� ) (cm)
Bi 5: 9WQKểNKếLOmỗQJP JWUHRYjRôXGmòLFởDOz[RQKẵFyN
1P7ù97&%QJmỏLWDNtFKWKtFKGDRíQJEàQJFiFKWUX\QFKRPPíWYQ
WếFFPVWKHRSKmkQJFởDWUộFOz[R&KẹQJếFWẹDíó97&%JếFWKỏLJLDQ
O~FPTXD97&%3KmkQJWUuQKGDRíQJFởDPOj
A: x=4cos(10t-
2
S
) (cm) B: x=4cos(10t+
2
�S
) (cm)
C: x=4cos( 10
2
t
�S
�� ) (cm) D: x=4cos( 10
2
t
S
) (cm)
7uPQKDQKPíWƠLOmỗQJFKmDELWWURQJELầXWKớFYWOờ
D&iFEjLW5SP3X
Bi 1: 76+ 7ƠLQkLFyJLDWếFWUẹQJWUmỏQJPV PíWFRQOF
kQYjPíWFRQOFOz[RQàPQJDQJGDR íQJLXKzDYòLFãQJWôQVế%LWFRQ
OFkQFyFKLXGjLFPYjOz[RFyíFớQ1P.KếLOmỗQJYWQKểFởDFRQ
OFOz[ROj
A:0,125 kg B:0,500 kg C:0,750 kg D:0.250 kg
�%�j�L���J�L�+�L����
Ta có 2
l
g
�S =2
m
k
�S
l m
g k
� o �
�x �1�K�±�S��
0.49
9,8 10
m
� �©�Q������������ 9,8 ALPHA CALC ALPHA ) 10 SHIFT
CALC =
0jQKuQK[XâWKLậQ; o ;OjƠLOmỗQJPFôQWuP
&KẹQiSiQ%
%jL76+0íWFRQOFkQFyFKLXGjLFPGDRíQJLX
34
KzDWƠLQkLFyJLDWếFWUẹQJWUmỏQJJOâ\2S &KXNuGDRíQJFởDFRQOFOj
A: 0,5 s B:2s C:1s D:2,2s
�%�j�L���J�L�+�L����
Ta có T= 2
l
g
�S �1�K�±�S���7�
1,21
2
10
�S
�x �1�K�±�S����ALPHA ) ALPHA CALC 2�S SHIFT 1,21 10 SHIFT CALC
=
0jQKuQK[XâWKLậQ; o OjJLiWUẽ7FôQWuP
&KẹQiSiQ'
E&iFEjLW5SY5QGmQJ
%jL76+ 0íWYWGDRíQJLXKzDYòLELrQíFPYjFhu kỡ
V4XmQJmỏQJYWLmỗFWURQJVOj
A:64cm B: 16cm C:32cm D:8cm
Bi 4: 0íW FKâW LầP �W�K�õ�F�� �K�L�Ë�Q�� �G�D�R�� �ÿ�Ý�Q�J�� �ÿ�L�Å�X�� �K�z�D�� �G�Ñ�F�� �W�K�H�R�� �W�U�é�F�� �2�[�� [RD\
TXDQK Yẽ WUt FkQ EàQJ 2 YòL FKX Nu 7 V WƠL WKỏL LầP1t FKâW LầP Fy WẹD í
1x FPYjYQWếF1v =4SFPV;iFẽQKELrQíFởDFKâWLầPWƠLWKỏLLầP1t l:
A: 5cm B: 6cm
C: 10cm D: 25cm
Bi 5: &RQOFOz[RJìPYWQKểNKếLOmỗQJP JYjOz[RFyíFớQJN
NtFKWKtFKFKRYWGDRíQJLXKzDYòLFkQQJ( P-.KLYWTXDOLí-1cm
WKuYQWếFOj-FPVíFớQJNFởDOz[ROj
A: 250N/m B:200N/m C:150N/m D:100N/m
�������������7�u�P���ÿ�L�Å�X���N�L�Ë�Q���N�t�F�K���W�K�t�F�K���E�D�Q���ÿ�«�X
�D�����&�i�F���E�j�L���W�5�S���P�3�X��
Bài 1: �7�u�P�� �ÿ�L�Å�X�� �N�L�Ë�Q�� �N�t�F�K�� �W�K�t�F�K�� �E�D�Q�� �ÿ�«�X�� �F�ë�D�� �Y�±�W�� �G�D�R�� �ÿ�Ý�Q�J�� �ÿ�L�Å�X�� �K�z�D�� �F�y��
�S�K�m�k�Q�J���W�U�u�Q�K���[� ����2 os( )
2
c t
�S
�S �� (cm).
�%�j�L���J�L�+�L����
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
35
�x MODE 2
�x SHIFT MODE 4
�x 4 2 SHIFT (-)
2
�S
= �P�j�Q���K�u�Q�K���K�L��Q��4 2i
Ta có
0
4 2
o
o
x a
v b� Z � S
� � ��°
�®
� ��
9\ ầ YW ó Yẽ WUtox UìL WUX\Q �F�K�R�� �Y�±�W�� �P�Ý�W�� �Y�±�Q�� �W�Õ�F��4 2ov �S� �F�P���V�� �W�K�H�R�� FKLX
õm.
Bi 2: 7DSKĐLWUX\QFKRYWPíWYQWếFEàQJEDRQKLrXầYWGDRíQJ
LXKzDFySKmkQJWUuQK[ 2 3 os(2 )
6
c t
S
(cm).
�%�j�L���J�L�+�L��
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2
�x SHIFT MODE 4
�x 2 3 SHIFT (-) -
6
�S
�[�X�©�W���K�L�Ë�Q����- 3i
Ta có
0 3
2 3o
x a
v b�Z
� ư
đ
9\WDSKĐLWUX\QFKRYWPíWYQWếF2 3ov WKHRFKLXGmkQJ
E&iFEjLW5SY5QGmQJ
Bi 3: 0íWYWGDRíQJLXKzDFySKmkQJWUuQK[ FRVtS FPNKLYW
FKmDEẽNtFKWKtFKGDRíQJYWFyOLíEàQJEDRQKLrX
iSiQ /LíEDQôXFởDYWOjFP
Bi 4:3KĐLWUX\QFKRYWPíWYQWếFEàQJEDRQKLrXầYWGDRíQJLX
KzDYòLSKmkQJWUuQK[ 5 2 os(2
4
c t
S
)(cm).
iSiQ v=10m/s
Bi 5: �7�u�P�� �ÿ�L�Å�X�� �N�L�Ë�Q�� �N�t�F�K�� �W�K�t�F�K�� �E�D�Q�� �ÿ�«�X�� �F�ë�D�� �Y�±�W�� �G�D�R�� �ÿ�Ý�Q�J�� �ÿ�L�Å�X�� �K�z�D�� �F�y��
36
�S�K�m�k�Q�J���W�U�u�Q�K�����[� �F�R�V��
5
2
6
t
�S
�S ) (cm).
iSiQ ầYWóYẽWUt
3
2
UìL WUX\QFKRYWPíWYQWếFSWKHRFKLXGmkQJ
%jLWSFKmkQJGzQJLậQ[RD\FKLX
7uPELầXWKớFXLWURQJPƠFKLậQ[RD\FKLX
D&iFEjLW5SP3X
%jL76+ằWLậQiS220 2 os100u c tS (V) vo hai ôXRƠQ
PƠFK PF �Q�Õ�L�� �W�L�Ã�S�� �J�×�P�� �ÿ�L�Ë�Q�� �W�U�ã��100R� � :���� �W�é�� �ÿ�L�Ë�Q�� Fy
410
2
C F
S
Yj FXíQ FĐP
WKXôQFy
1
L H
S
%LầXWKớFFmỏQJíGzQJLậQWURQJRƠQPƠFKOj
A: 2,2cos(100 )( )
4
i t A
�S
�S� � � B: 2,2 2 cos(100 )( )
4
i t A
�S
�S� � �
C: 2,2cos(100 )( )
4
i t A
�S
�S� � � D: 2,2 2 cos(100 )( )
4
i t A
�S
�S� � �
�%�j�L���J�L�+�L��
Ta có: 4
1 1
200
10
100 .
2
CZ
C�Z �S
�S
��� � � �:
1
100 . 100LZ L� Z � S
�S
� � � �:
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Ñ�D �ÿ�Ý���F�õ�F��r �I�‘ )
�x SHIFT MODE 3 ���F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tìm i: 220 2 SHIFT (-) 0 �y ( 100+ (100 - 200) SHIFT ENG ) =
�0�j�Q���K�u�Q�K���K�L��Q���W�K�����
11
45
5
�‘
�9�±�\�� 2,2cos(100 )( )
4
i t A
�S
�S� � �
�&�K�Ñ�Q���ÿ�i�S���i�Q���$
37
Bi 2: 0ƠFKLậQ[RD\FKLXJìPPíWLậQWUóWKXôQ50R :PíWFXíQWKXôQ
FĐPFyKậVếWừFĐP
1
L H
S
YjPíWWộLậQFyLậQGXQJ
42.10
C F
S
PFQếL
WLS%LWUàQJGzQJLậQTXDPƠFKFếGƠQJ5cos100 ( )i t AS %LầXWKớFLậQiS
WớFWKỏLJLúDKDLôXPƠFKLậQ
A: 250cos(100 )( )
4
u t V
�S
�S� � � B: 250cos(100 )( )
4
u t V
�S
�S� � �
C: 250 2 cos(100 )( )
4
u t V
�S
�S� � � D: 250 2 cos(100 )( )
4
u t V
�S
�S� � �
�%�j�L���J�L�+�L:
Ta có: 4
1 1
50
2.10
100 .
CZ
C�Z �S
�S
��� � � �:
1
100 . 100LZ L� Z � S
�S
� � � �:
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ �����������F�j�L���W�Ñ�D���ÿ�Ý���F�õ�F��r �I�‘ )
�x SHIFT MODE 3 ���F�K�Ñ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tìm u: 5 SHIFT (-) 0 �u ( 50 + (100 - 50) SHIFT ENG ) =
�0�j�Q���K�u�Q�K���K�L�Ç�Q���W�K�Ï����250 2 45�‘
�9�±�\�� 250 2 cos(100 )( )
4
u t V
�S
�S� � �
�&�K�Đ�Q���ÿ�i�S���i�Q���&
Bài 3: �P�Ý�W�� �P�¥�F�K�� �ÿ�L�Ë�Q�� �[�R�D�\�� �F�K�L�Å�X�� �5�/�&�� �N�K�{�Q�J�� �S�K�k�Q�� �Q�K�i�Q�K�� �F�y��100R� � :,
410
C F
�S
��
� ,
2
L H
�S
� �����&�m�á�Q�J���ÿ�Ý���G�z�Q�J���ÿ�L�Ë�Q���W�U�R�Q�J���P�¥�F�K���F�y���G�¥�Q�J��
2 2cos100 ( )i t AS %LầXWKớFLậQiSWớFWKỏLKDLôXPƠFKOjFmỏQJíGzQJ
LậQWURQJPƠFKFyGƠQJ
A: 400 5 cos(100 )( )
4
u t V
�S
�S� � � B: 400 5 cos(100 )( )
4
u t V
�S
�S� � �
38
C: 400cos(100 )( )
4
u t V
�S
�S� � � D: 400cos(100 )( )
4
u t V
�S
�S� � �
�%�j�L���J�L�+�L��
Ta có: 4
1 1
100
10
100 .
CZ
C�Z �S
�S
��� � � �:
2
100 . 200LZ L� Z � S
�S
� � � �:
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Ñ�D���ÿ�Ý���F�õ�F��r �I�‘ )
�x SHIFT MODE 3 ���F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tìm u: 2 2 SHIFT (-) 0 �u ( 100+ (200 - 100) SHIFT ENG ) =
�0�j�Q���K�u�Q�K���K�L�Ç�Q���W�K�Ï����400 45�‘
�9�±�\�� 400cos(100 )( )
4
u t V
�S
�S� � �
�&�K�Đ�Q���ÿ�i�S���i�Q���'
Bài 4: �&�K�R���P�¥�F�K���ÿ�L�Ë�Q���[�R�D�\���F�K�L�Å�X���F�y��40R� � :,
1
L H
�S
� ,
410
0,6
C F
�S
��
� �����0�³�F��
�Q�Õ�L�� �W�L�Ã�S�� �ÿ�L�Ë�Q�� �i�S�� ���� �ÿ�«�X�� �P�¥�F�K��100 2 os100 ( )u c t V�S� ���� �&�m�á�Q�J�� �ÿ�Ý�� �G�z�Q�J�� �ÿ�L�Ë�Q�� �T�X�D��
�P�¥�F�K���O�j��
A: 2,5cos(100 )( )
4
i t A
�S
�S� � � B: 2,5cos(100 )( )
4
i t A
�S
�S� � �
C: 2cos(100 )( )
4
i t A
�S
�S� � � D: 2cos(100 )( )
4
i t A
�S
�S� � �
�%�j�L���J�L�+�L����
Ta có: 4
1 1
60
10
100 .
0,6
CZ
C�Z �S
�S
��� � � �:
1
100 . 100LZ L� Z � S
�S
� � � �:
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Ñ�D���ÿ�Ý���F�õ�F��r �I�‘ )
39
�x SHIFT MODE 3 ���F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tìm i: 100 2 SHIFT (-) 0 �y ( 40+ (100 - 60) SHIFT ENG ) =
Mà�Q���K�u�Q�K���K�L�Ç�Q���W�K�Ï����
5
45
2
� ‘ � �
�9�±�\�� 2,5cos(100 )( )
4
i t A
�S
�S� � �
&KẹQiSiQ%
E&iFEjLW5SY5QGmQJ
Bi 5: &KRRƠQPƠFK[RD\FKLXJìP30R : YjFXíQGk\WKXôQFĐPFy
íWừFĐP/
3
S
+PFQếLWLSằWYjRKDLôXRƠQPƠFKPíWKLXLậQWK[RD\
FKLX60 2 sin(100 )
4
u t
S
S 99LWELầXWKớFFmỏQJíGzQJLậQTXDPƠFK
iSiQ 2sin(100 )( )
2
i t A
S
S
Bi 6: 0íWRƠQPƠFKLậQJìP50R : PFQếLWLSYòLFXíQFĐPWKXôQ
cú
1
2
L H
S
ằW YjR KDL ôX �ÿ�R�¥�Q�� �P�¥�F�K�� �P�Ý�W�� �ÿ�L�Ë�Q�� �i�S�� �[�R�D�\�� �F�K�L�Å�X��
100 2 os(100 )( )
4
u c t V
S
S 9LWELầXWKớFFmỏQJíGzQJLậQTXDRƠQPƠFK
iSiQ 2cos(100 )( )
2
i t A
�S
�S� � �
Bài 7: �&�K�R���P�¥�F�K���ÿ�L�Ë�Q���[�R�D�\���F�K�L�Å�X���F�y��30R� � :,
1
L H
�S
� ,
410
0,7
C F
�S
��
� �����+�L��X��
�ÿ�L�Ë�Q�� �W�K�Ã�� �K�D�L�� ôX PƠFK Oj120 2 os100 ( )u c VS �W�K�u�� �F�m�á�Q�J�� �ÿ�Ý�� �G�z�Q�J�� �ÿ�L�Ë�Q�� �W�U�R�Q�J��
�P�¥�F�K���O�j���E�D�R���Q�K�L�r�X�"
���i�S���i�Q�� 4cos(100 )( )
4
i t A
�S
�S� � �
���������������%�j�L���W�R�i�Q���F�Ý�Q�J���ÿ�L�Ë�Q���i�S��
�D�����&�i�F���E�j�L���W�5�S���P�3�X��
40
Bi 1: &KRPƠFKJìPRƠQ$0FKớD5&PFQếLWLSYòLRƠQ0%FKớD
FXíQFĐP/U7uPABu ELW
100 2 os(100 )( )
6MBu c t V
�S
�S� � �
�%�j�L���J�L�+�L��
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Ñ�D���ÿ�Ý���F�õ�F��r �I�‘ )
�x SHIFT MODE 3 ���F�K�Ñ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tính ABu : 100 2 SHIFT (-) - 60 + 100 2 SHIFT (-) 30 =
�0�j�Q���K�u�Q�K���K�L�Ë�Q����200 15� ‘ � �
�9�±�\�� 200cos(100 )( )
12ABu t v
S
S
Bi 2: 1XằWYjRKDLôXPíWPƠFKLậQFKớDPíWLậQWUóWKXôQYjPíW
FXíQFĐPWKXôQPFQếLWLSPíWLậQiS[RD\FKLXFyELầXWKớF
100 2 os( )( )
4
u c t V
�S
�Z� � � thì �N�K�L�� �ÿ�y�� �ÿ�L�Ë�Q�� �i�S�� �J�L�ó�D�� �K�D�L�� �ÿ�«�X�� �ÿ�L�Ë�Q�� �W�U�ã�� �W�K�X�«�Q�� �F�y�� ELầX
WKớF100cos( )( )Ru t VZ %LầXWKớFLậQiSJLúDKDLôXFXíQFĐPWKXôQOj
A: 100cos( )( )
2Lu t V
�S
�Z� � � B: 100 2 cos( )( )
4Lu t V
�S
�Z� � �
C: 100cos( )( )
4Lu t V
�S
�Z� � � D: 100 2 cos( )( )
2Lu t V
�S
�Z� � �
�%�j�L���J�L�+�L��
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Ñ�D���ÿ�Ý���F�õ�F��r �I�‘ )
�x SHIFT MODE 3 ���F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tính Lu : 100 2 SHIFT (-) 45 �± 100 SHIFT (-) 0 =
100 2 os(100 )( )
3AMu c t V
�S
�S� � �
41
�0�j�Q���K�u�Q�K���K�L�Ë�Q����100 90�‘
�9�±�\�� 100cos( )( )
2Lu t V
�S
�Z� � �
�&�K�Ñ�Q���ÿ�i�S���i�Q���$
Bài 3: �1�Ã�X�� �ÿ�»�W�� �Y�j�R�� KDL ôX RƠQ PƠFK FKớD PíW LậQ WUó WKXôQ Yj �P�Ý�W�� �W�é��
�G�L�Ë�Q���P�³�F���Q�Õ�L���W�L�Ã�S���P�Ý�W���ÿ�L�Ë�Q���i�S���[�R�D�\���F�K�L�Å�X���F�y���E�L�Ç�X���W�K�í�F��100 2 os( )( )
4
u c t V
�S
�Z� ,
NKLyLậQiSKDLôXLậQWUóWKXôQFyELầXWKớF100cos( )( )Ru t VZ %LầXWKớF
LậQiSJLúDKDLôXWộLậQOj
A: 100 os( )( )
2Cu c t V
�S
�Z� � � B: 100 2 cos( )( )
4Cu t V
�S
�Z� � �
C: 100cos( )( )
4Cu t V
�S
�Z� � � D: 100 2 cos( )( )
2Cu t V
�S
�Z� � �
�%�j�L���J�L�+�L��
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Đ�D���ÿ�Ý���F�õ�F��r �I�‘ )
�x SHIFT MODE 3 ���F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tính Cu : 100 2 SHIFT (-) �± 45 - 100 SHIFT (-) 0 =
�0�j�Q���K�u�Q�K���K�L�Ë�Q����100 90� ‘ � �
�9�±�\�� 100cos( )( )
2Cu t V
�S
�Z� � �
�&�K�Ñ�Q���ÿ�i�S���i�Q���$
%jL76+ ằWLậQiS[RD\FKLXYjRKDLôXRƠQPƠFKFy R, L,
&QếLWLS%LW10R :FXíQFĐPWKXôQFy
1
10
L H
S
WộLậQFy
310
2
C F
S
v
LậQiSJLúDKDLôXFXíQFĐPOj20 2 os(100 )( )
2Lu c t V
S
S %LầXWKớFLậQiS
JLúDKDLôXRƠQPƠFKOj
A: 40cos(100 )( )
4
u t V
�S
�S� � � B: 40 2 cos(100 )( )
4
u t V
�S
�S� � �
42
C: 40cos(100 )( )
4
u t V
�S
�S� � � D: 40 2 cos(100 )( )
4
u t V
�S
�S� � �
�%�j�L���J�L�+�L��
Tính: 10LZ � � : 20CZ � � :
Ta có:
.
. L
L
U Z
u i Z
Z
� �
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 (màn �K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Ñ�D���ÿ�Ý���F�õ�F��r �I�‘ )
�x SHIFT MODE 3 ���F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tính u: 20 2 SHIFT (-) 90 �u ( 10 + ( 10 �± 20 ) SHIFT ENG ) �y ( 10
SHIFT ENG ) =
�0�j�Q���K�u�Q�K���K�L�Ç�Q���W�K�Ï����40 45�‘
�9�±�\�� 40cos(100 )( )
4
u t V
�S
�S� � �
�&�K�Đ�Q���ÿ�i�S���i�Q���$
Bài 5: �0�Ý�W�� �ÿ�R�¥�Q�� PƠFK JìP Wộ LậQ & Fy GXQJ NKiQJ100CZ : Yj PíW
FXíQGk\FyFĐPNKiQJ200LZ : PFQếLWLSQKDXLậQiSằWWƠLKDLôXFXíQ
FĐP Fy �E�L�Ç�X�� �W�K�í�F��100cos(100 )( )
6Lu V
�S
�S� � ����� �%�L�Ç�X�� �W�K�í�F�� LậQ iS ó KDL ôX RƠQ
PƠFKOj
A: 50cos(100 )( )
3
u t V
�S
�S� � � B:
5
50cos(100 )( )
6
u t V
�S
�S� � �
C: 100cos(100 )( )
2
u t V
�S
�S� � � D:
2
50cos(100 )( )
3
u t V
�S
�S� � �
�%�j�L���J�L�+�L��
Ta có: . .L
L
U
u i Z Z
Z
� �
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ���F�j�L���W�Ñ�D���ÿ�Ý���F�õ�F��r �I�‘ )
43
�x SHIFT MODE 3 ���F�K�Đ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x Tính u: 100 SHIFT (-) 30 �u ( 200 �± 10 ) SHIFT ENG ) �y ( 200 SHIFT
ENG ) =
�0�j�Q���K�u�Q�K���K�L�Ç�Q���W�K�Ï����50 120�‘
�9�±�\��
2
50cos(100 )( )
3
u t V
�S
� S � S� �
&KẹQiSiQ'
b. Cỏc bi t5SY5QGmQJ
Bi 6: RƠQPƠFK$%FyLậQWUóWKXôQFXíQGk\WKXôQYjWộLậQPFQếL
WLS 0 Oj PíW LầP QàP WUrQ RƠQ $% YòL LậQ iS10cos100 ( )AMu t V�S� và
10cos(100 )( )
3MBu t V
�S
�S� � ������7�u�P���E�L�Ç�X���W�K�í�F���ÿ�L�Ë�Q���i�S��ABu ?
A: 20 2 os(100 )( )
3ABu c t V
�S
�S� � � B: 20 3 os(100 )( )
3ABu c t V
�S
�S� � �
C: 10 3 os(100 )( )
6ABu c t V
�S
�S� � � D: 10 3 os(100 )( )
6ABu c t V
S
S
Bi 7: &KRRƠQPƠFK$0FKớDPíWLậQWUóWKXôQQếLWLSYòLPƠFK0%
FKớDFXíQFĐPFyLậQWUóUELWLậQiSWớFWKỏLJLúDFiFLầP$Yj0, M v B
�F�y�� �G�¥�Q�J����15 2 os(200 )( )
3AMu c t V
�S
�S� � � và 15 2 os(200 )( )MBu c t V�S� ���� �%�L�Ç�X�� �W�K�í�F��
�ÿ�L�Ë�Q���i�S���J�L�ó�D���$���Y�j���%���O�j��
A: 15 6 os(200 )( )
6ABu c t V
�S
�S� � � B: 15 6 os(200 )( )
6ABu c t V
�S
�S� � �
C: 15 2 os(200 )( )
6ABu c t V
�S
�S� � � D: 15 6 os(200 )( )ABu c t V�S�
���������������%�j�L���W�R�i�Q���K�Ý�S���ÿ�H�Q
�D�����&�i�F���E�j�L���W�5�S���P�3�X��
Bài 1: �0�Ý�W���K�Ý�S���ÿ�H�Q���F�K�í�D���K�D�L���W�U�R�Q�J���E�D���S�K�«�Q���W�đ���5���/���&���P�³�F���Q�Õ�L���W�L�Ã�S�����1�Ã�X���ÿ�»�W��
�Y�j�R�� �K�D�L�� �ÿ�«�X�� �ÿ�R�¥�Q�� �P�¥�F�K�� �P�Ý�W�� �ÿ�L�Ë�Q�� �i�S�� �[�R�D�\�� �F�K�L�Å�X��100 2 cos(100 )( )
4
u t V
�S
�S� � � thì
44
FmỏQJíGzQJLậQTXDKíSHQOjL FRVSW$RƠQPƠFKFKớDSKôQWủ
QjR"*LiWUẽFởDFiFƠLOmỗQJy
%jLJL+L
4X\WUuQKEâPPi\
x MODE 2 PjQKuQK[XâWKLậQ&03/;
x SHIFT MODE �’ 3 1 ầFKX\ầQYGƠQJFiFDEL
x SHIFT MODE 3 FKẹQkQYẽROjí'
x 100 2 SHIFT ( )�� 45 �y 2 SHIFT ( )�� 0
�0�j�Q���K�u�Q�K���K�L��Q���W�K��������������L
�9�±�\���K�Ý�S���ÿ�H�Q���F�K�í�D R = 50 : FKớD/YòL=L=50 :
Bi 2: 0íWKíSHQFKớDKDLWURQJEDSKôQWủ5/&PFQếLWLS1XằW
YjR KDL ôX RƠQ PƠFK PíW LậQ iS [RD\ FKLX)V)(
4
t100cos(2100u
S
S thỡ
FmỏQJíGzQJLậQTXDKíSen l i = 2cos(100SW$RƠQPƠFKFKớDSKôQWủ
QjR"*LiWUẽFởDFiFƠLOmỗQJy
%jLJL+L
4X\WUuQKEâPPi\
x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 1 ầFKX\ầQYGƠQJFiFDEL
x SHIFT MODE 3 FKẹQkQYẽROjí'
�x 100 2 SHIFT ( )�� -45 �y 2 SHIFT ( )�� 0
�0�j�Q���K�u�Q�K���K�L��Q���W�K�������-50i
�9�±�\���K�Ý�S���ÿ�H�Q���F�K�í�D���5��� ���������: , ZC = 50�:
Bi 3: 0íWKíSHQFKớDKDLWURQJEDSKôQWủ5/&PFQếLWLS1XằW
YjR KDL ôX RƠQ PƠFK PíW LậQ �i�S�� �[�R�D�\�� �F�K�L�Å�X��)V)(
6
t100cos(6200u
�S
���S� thì
�F�m�á�Q�J�� �ÿ�Ý�� �G�z�Q�J�� �ÿ�L�Ë�Q�� �T�X�D�� �K�Ý�S�� �ÿ�H�Q�� �O�j��)
6
t100cos(22i
�S
���S� ���$������ ���R�¥�Q�� �P�¥�F�K�� �F�K�í�D��
45
SKôQWủQjR"*LiWUẽFởDFiFƠLOmỗQJy
%jLJL+L
4X\WUuQKEâPPi\
x MODE 2 PjQKuQK[XâWKLậQ&03/;
x SHIFT MODE 3 1 ầFKX\ầQYGƠQJFiFDEL
x SHIFT MODE 3 ���F�K�Ñ�Q���ÿ�k�Q���Y�Ï���ÿ�R���O�j���ÿ�Ý���'��
�x 200 6 SHIFT ( )�� -30 �y 2 2 SHIFT ( )�� 0
�0�j�Q���K�u�Q�K���K�L��Q���W�K��� 50 3+150i
�9�±�\���ÿ�R�¥�Q���P�¥�F�K���F�K�í�D���5��� ��350 �: và ZL = 150�:
Bi 4: KíSNtQ;FKFKớDWURQJSKôQWủ5/&ằWYjRKDLôXRƠQ
PƠFKLậQiS[RD\ FKLXXAB = 200cos(100SW 9 WKuELầXWKớF FmỏQJíGzQJ
LậQWURQJPƠFKOjL 2 cos(100St-
3
S
) $;iFẽQKSKôQWủ KíS;YjJLiWUẽ
FởDQy
%jLJL+L
4X\WUuQKEâPPi\
x MODE 2 PjQKuQK[XâWKLậQ&03/;
�x SHIFT MODE �’ 3 1 ầFKX\ầQYGƠQJFiFDEL
x SHIFT MODE 3 FKẹQkQYẽROjí'
x 200 2 SHIFT ( )�� 30 �y 2 2 SHIFT ( )�� -60
x 0jQKuQKKLầQWKẽL
9\RƠQPƠFKFKớD/=L = 100 :
E&iFEjLW5SY5QGmQJ
Bi 50íWKíSHQFKớDPíWWURQJEDSKôQWủ5/&PFQếLWLS1XằWYjR
KDLôXRƠQPƠFKPíWLậQiS[RD\FKLXXAB = 200 2 cos(100St -
3
S
) (V) thì
46
�F�m�á�Q�J�� �ÿ�Ý�� �G�z�Q�J�� �ÿ�L�Ë�Q�� �T�X�D�� �K�Ý�S�� �ÿ�H�Q�� �O�j��2cos(100 )
3
i t
�S
�S� � � $ RƠQ PƠFK FKớD
SKôQWủQjR"*LiWUẽFởDFiFƠLOmỗQJy
iSiQ: R=200:
Bi 6: 0íWKíSHQFKớDPíWWURQJEDSKôQWủ5/&PFQếLWLS1XằW
YjR KDL ôX RƠQ PƠFK PíW LậQ iS [RD\ FKLX �XAB = 120 2 cos(100�St +
310
4�S
��
)
���9�������W�K�u���F�m�á�Q�J���ÿ�Ý���G�z�Q�J���ÿ�L�Ë�Q���T�X�D���K�Ý�S���ÿ�H�Q���O�j��3cos(100 )
2
i t
�S
�S� $RƠQPƠFK
FKớDSKôQWủQjR
iSiQ: R = 40 : , C =
310
4S
(F)
Bi 8: FKRKDLRƠQPƠFKJìPSKôQWủ;
WKầOj5/KRằF&FKRELWKLậXLậQWKJLúDôXRƠQPƠFKOjXAB = 200 2
cos(100St) (v) , i = 2 2cos(100St-
6
S
$&KRELW;
*LiWUẽFởDFiFSKôQWủâ\
iSiQ: 50 3R� � : và L =
1
2�S
(H)
7uPKậVếF{QJVXâWWURQJPƠFKLậQ[RD\FKLX
D&iFEjLW5SP3X
Bi 1: FKRRƠQPƠFK$%JìP$0Yj0%PFQếLWLSRƠQ$0JìPLậQ
WUóWKXôQ5 : YjTXQFĐPWKXôQ/
1
S
(H)
RƠQ0%OjWộLậQFyLậQGXQJ&ELầXWKớFLậQiS WUrQPƠFK$0Yj0%OôQ
OmỗW Oj100 2 cos(100 )( )
4AMU t V
S
S � � và 200cos(100 )( )
2MBU t V
�S
�S� � Kậ Vế
F{QJVXâWWUrQRƠQPƠFK$%Oj
A.
3
os
2
c M B.
2
os
2
c M C. os 0,5c �M� D. os 0,75c �M�
47
Bài �J�L�+�L����
Ta có : AMZ =(100+100i)
�7�Ù�Q�J���W�U�ã���S�K�í�F���F�ë�D���ÿ�R�¥�Q���P�¥�F�K���$�%���O�j����
( )
. (1 ).AB AM MB MB
AB AM AM
AM AM
U U U U
Z Z Z
i U U
��
� � � ��
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 2 ầFKX\ầQYGƠQJFiFDEL
x SHIFT MODE 3 FKẹQkQYẽROjí'
x %âP
200 90
1
100 2 45
� ‘ � �
��
�‘
) �u (100+100i) = 141.42 45� ‘ � �
�x �%�©�P��SHIFT 2 1 = - 45
x %âPcos(ans) =
0jQKuQKKLầQWKẽ
2
2
9\KậVếF{QJVXâWFởDPƠFKOj
2
2
&KẹQiSiQ%
Bi 2 : &KRRƠQPƠFK$%PFQếLWLSJìPFiFSKôQWủLậQWUóWKXôQTXQ
FĐPYjWộLậQ$%JìP$0Yj0%PFQếLWLSRƠQ$0JìPLậQWUóWKXôQ5
= 50 : YjWộLậQFy dung khỏng 50: ELầXWKớFLậQiSWUrQPƠFK$%Yj0%
OôQ OmỗW Oj80cos(100 )( )AMU t V�S� và 100cos(100 )( )
2MBU t V
�S
�S� � Kậ Vế F{QJ
VXâWWUrQRƠQPƠFK$%Oj
A. os 0,99c M B. os 0,84c �M� C. os 0,86c �M� D. os 0,95c �M�
�%�j�L���J�L�+�L��
Ta có :
(50 50 )AMZ i� � �
�7�Ù�Q�J���W�U�ã���S�K�í�F���F�ë�D���ÿ�R�¥�Q���P�¥�F�K���$�%���O�j����
48
( )
. (1 ).AB AM MB MB
AB AM AM
AM AM
U U U U
Z Z Z
i U U
��
� � � ��
�4�X�\���W�U�u�Q�K���E�©�P���P�i�\��
�x MODE 2 ���P�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q���&�0�3�/�;��
�x SHIFT MODE �’ 3 1 ầFKX\ầQYGƠQJFiFDEL
x SHIFT MODE 3 FKẹQkQYẽROjí'
x %âP
100 90
80 0
) �u (50-50i) =
25 82
6.343
2
�‘
�x �%�©�P��SHIFT 2 1 =
�0�j�Q���K�u�Q�K���[�X�©�W���K�L�Ë�Q������������
�x �%�©�P cos(ans) =
0jQKuQK[XâWKLậQ
9\KậVếF{QJVXâWFởDPƠFKOjos 0,99c M
&KẹQiSiQ$
%jL 76+ RƠQ PƠFK $% JìP RƠQ PƠFK $0 Yj 0% PF
QếL WLS RƠQ $0 JìP LậQ WUó WKXôQ1 40R � :���P�³�F�� �Q�Õ�L�� �W�L�Ã�S�� �Y�ß�L �W�é�� �ÿ�L�Ë�Q�� �F�y�� �ÿ�L�Ë�Q��
dung
310
4
C
�S
��
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