Co-So-Ky-Thuat-Dien__Bai-Tap-Chuong-5 - [Cuuduongthancong.com].Pdf

5.1/

  x1
  x2

a/ Đặt 

0, 04

ta có :

dx1
 x2
dt

(1)

d2
d
x1  0, 004 x1  1  2sin x1 (2)
2
dt
dt

.c
om

d2
d
(2)=> 0, 04 2 x1  0, 004 x1  2 co x1x1
dt

dt
d
(1)=>
x1  x2 x1
dt
x  x1
.

 x1  x2

an

ng

th

. 
0
1   x1 
 x1   

 .   50cos x1 0,1  x2 
 x2 
d2
d
0, 04 x1 _ 0,004 x1  2 cos x1x1
dt
dt

co

ng

 .
  x1  x2

.
0,04 x2  0,004x2  2 cos x1x1

du
o

0, 04x2  0,04x1  2cos x1x1

u

  x. 
0
1   x1 

  .1   

  0,1  50 cos x1 0   x2 

x
 2

cu

b/ equilibrium points (điểm cân bằng)

1  2sin   0  sin  

1
2


30 0
f  0
0
0
180  30  150
 tại   300

d2
d
0,04
x1  0, 004 x1   3x1

dt
dt

.

  x1  x2
Tại   1500

CuuDuongThanCong.com

/>


d2
d
0,04
x1  0,004 x1  3x1

dt
dt

 .
  x1  x2
5.2/
a/

Te 

1 2
 I  0, 2sin   0,1sin 2  
2

Equilibrium points

.c
om

Tm Te  0
1
1
  0, 2sin   0,1sin 2   sin 

2
6
 0,3sin 2  0, 4sin 
 6sin  cos   4sin   0

ng

  00

0
  48,19

co

b/
V(x)=U(x)-Win

th

an

u ( x)
 Mgl sin 
x
U  x    Mgl cos 

 V ( x)   Mgl cos   3Mgl  0,1  0, 2 cos   0, 05cos 2 

cu

u

du
o

ng

V  
  Mgl sin   3Mgl  0, 2sin   0,1sin  

 2V  
  Mgl cos   3Mgl  0, 2cos   0, 2cos 2 
 2
 2V  
 0  stable
  0
 2
 2V  
0
 0  unstable
  48,19 
 2
c/
V    Mgl cos   3Mgl  0,1  0, 2 cos   0,05cos 2   C
d/
5.3/

CuuDuongThanCong.com

/>

W 'm 9 2 2
 Ax i
x
2
9
f e  kx  Ax 2i 2  kx
2
x  0

 x  2k 2  1
9 Ai
2

fe

b/

U  x 
x2
 Kx  U  x   K
x
2
V  x   U  x   W 'm

.c
om



x2 3 3 2
K
 Ax i
2 2

ng

5.4/
a/

co

x3  x  0

an

x  0

 x  1
b/ Phương trình đặc trưng

du
o

 x  C1e0,618t  C2e 1,62t

ng

th

2   1  0
  0,618
 1
2  1,62
x  0   0,5  C1  C2  0,5
.

u

 x  0  0, 618C1  1, 62C2  0

cu

C1  0,362

C2  0,138
x  t   0,362e0,618t  0,138e1,62t
 Tại (1,0):
Phương trình đặc trưng:

 21  1  2  0
 1,2  0,5  1,323 j
x  t   e0,5t (C1 cos1,323t  C2 sin1,323t )
C1  0,5

C2  0,189

CuuDuongThanCong.com

/>

5.5/

0,1

d2
d
  0,5   4 cos 
2
dt
dt

.

   
.

0,1 v  0,5  4 cos 
1
0 

.c
om

.  
0
 x1   
 x2   40cos 

5.6/

an

cu

x  0

K
x  2
9i


u

 x  9 xi 2  K   0

du
o

d 2x
M 2  f e  K  x  x0 
dt
W 'm
W 'm 
 9 x 2i 2
x
e
f  Wx

co

dx
di
 6 x3
dt
dt

th

 30i  18 x 2i

ng


t

ng

V  t   30i 

CuuDuongThanCong.com

/>