Tải bản đầy đủ (.pdf) (56 trang)

Khai thác tính năng của máy tính casio fx570es trong giải một số bài tập chương dao động cơ và dòng điện xoay chiều thuộc chương trình vật lý 12

Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (661.99 KB, 56 trang )

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


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

��

� (F). RƠQPƠFK0%JìPLậQWUóWKXôQ5PFQếLWLSYòLFXíQ

FĐP ằWYjR$%LậQiS[RD\ FKLXFyJLi WUẽKLậXGộQJYj WôQVếNK{QJLWKu

LậQiSWớFWKỏLóôXRƠQPƠFK$0Yj0%OôQOmỗWOj
7

50 2 cos(100 )
12AMu t
�S

�S� � � (V)


150cos(100 )MBu t�S� (V)

+ậVếF{QJVXâWFởDRƠQPƠFK$%Oj

A. 0,84 B. 0,71 C. 0,86 D. 0,95

�%�j�L���J�L�+�L��

Ta có : (100 100 )AMZ i� � �

�7�Ù�Q�J���W�U�ã���S�K�í�F���F�ë�D���ÿ�R�¥�Q���P�¥�F�K���$�%���O�j:








49

( )
. (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
150 0

1
50 2 105

�‘
��

� ‘ � �
�u (40-40i) = 118.685 32.600�‘

�x �%�©�P��SHIFT 2 1 =

Màn hình xu�©t hi�Ën 32.6


�x B�©m cos(ans) =

Mn hỡnh hiần thẽ 0.84

9\KậVếF{QJVXâWFởDPƠFKOj

&KẹQiSiQ

×