Tema_No_12
.pdfa 0.1
r 0.4
b 1
Given
d2 |
x(t) r d |
x(t) |
x(t) |
|
b (a |
|
x(t) |
|
) d x(t) |
||
|
|
|
|||||||||
|
|
|
|
|
|||||||
|
|
|
|
|
|||||||
dt |
2 |
dt |
|
|
|
|
|
|
|
dt |
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
x(0) |
0.01 |
|
|
|
|
|
x'(0) |
0 |
|
|
|
|
|
x Odesolve(t100) |
|
|
||||
t 0.1 0.2 100 |
|
|
|
|||
|
0 |
.4 |
|
|
|
|
|
0 |
.2 |
|
|
|
|
x(t) |
|
0 |
20 |
40 |
60 |
80 |
|
|
|||||
|
0.2 |
|
|
|
|
|
|
0 |
.4 |
|
|
|
|
|
|
|
|
|
t |
|
|
|
0 |
.4 |
|
|
|
|
0 |
.2 |
|
|
d x(t) |
0.4 |
0.2 |
|
|
|
dt |
0 |
0.2 |
0.4 |
||
|
|
0.2 |
|
|
|
|
|
0.4 |
|
|
|
|
|
|
x(t) |
|
|
a 0.1
r 0.05
b 0.04
Given
d2 |
x(t) r d |
x(t) |
x(t) |
|
b (a |
|
x(t) |
|
) d x(t) |
||
|
|
|
|||||||||
|
|
|
|
|
|||||||
|
|
|
|
|
|||||||
dt |
2 |
dt |
|
|
|
|
|
|
|
dt |
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
x(0) 0.01
x'(0) 0
x Odesolve(t100)
t 0.1 0.2 100
|
|
|
|
0.01 |
|
|
0.01 |
|
|
|
|
|
5 10 3 |
|
|
5 10 3 |
|
|
|
|
|
|
|
x(t) |
|
d |
x(t) |
|
|
0 20 40 60 80 |
dt |
|
|
|
|
|
0.01 |
0 |
0.01 |
||
|
|
||||
|
5 10 3 |
|
|
5 10 3 |
|
|
0.01 |
|
|
0.01 |
|
|
|
|
|
|
|
|
t |
|
|
|
|
|
|
|
|
x(t) |
|
a 2
r 0.25
b 0.1
Given
d2 |
x(t) r d |
x(t) |
x(t) |
|
b (a |
|
x(t) |
|
) d x(t) |
||
|
|
|
|||||||||
|
|
|
|
|
|||||||
|
|
|
|
|
|||||||
dt |
2 |
dt |
|
|
|
|
|
|
|
dt |
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
x(0) 0.01
x'(0) 0
x Odesolve(t100)
t 0.1 0.2 100
|
|
|
|
0.01 |
|
|
0.01 |
|
|
|
|
|
5 10 3 |
|
|
5 10 3 |
|
|
|
|
|
|
|
x(t) |
|
d |
x(t) |
|
|
0 20 40 60 80 |
dt |
|
|
|
|
|
0.01 |
0 |
0.01 |
||
|
|
||||
|
5 10 3 |
|
|
5 10 3 |
|
|
0.01 |
|
|
0.01 |
|
|
|
|
|
|
|
|
t |
|
|
|
|
|
|
|
|
x(t) |
|
a 0.2
r 0.01
b 0.1
Given
d2 |
x(t) r d |
x(t) |
x(t) |
|
b (a |
|
x(t) |
|
) d x(t) |
||
|
|
|
|||||||||
|
|
|
|
|
|||||||
|
|
|
|
|
|||||||
dt |
2 |
dt |
|
|
|
|
|
|
|
dt |
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
x(0) 0.01
x'(0) 0
x Odesolve(t100)
t 0.1 0.2 100
|
|
|
|
|
|
|
|
|
1 |
|
0.5 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.5 |
|
0 |
20 |
40 |
60 |
80 |
d |
x(t) |
|
|
|
|
x(t) |
|
|
|
|
|
1 |
0.5 |
|
|
|
|
|
|
|
dt |
|
0 |
0.5 |
|||
|
|
|
|
|
|
|||||
0.5 |
|
|
|
|
|
|
|
|
0.5 |
|
|
|
|
|
|
|
|
|
|
|
|
1 |
|
|
|
|
|
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
t |
|
|
|
|
|
x(t) |
|
|
|
|
|
|
|
|
|
|
|
a 0.1
k 1
Given
d2 |
x(t) k x(t) |
|
a 1 |
x(t)2 d x(t) |
|
|
|||
|
|
|||
2 |
|
|
|
dt |
dt |
|
x(0) 0.01
x'(0) 0
x Odesolve(t200)
t 0.1 0.2 200
2 |
|
|
|
|
|
|
|
3 |
|
|
1 |
|
|
|
|
|
|
|
2 |
|
|
|
|
|
|
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
x(t) |
|
|
|
|
d |
x(t) |
2 |
1 1 0 |
|
|
0 |
50 |
100 |
150 |
200 |
dt |
|
1 |
2 |
||
1 |
|
|
|
|
|
|
|
2 |
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
|
|
|
|
|
|
|
3 |
|
|
|
|
t |
|
|
|
|
|
x(t) |
|
|
a 0.1
k 0.1
Given
d2 |
x(t) k x(t) |
|
a 1 |
x(t)2 d x(t) |
|
|
|||
|
|
|||
2 |
|
|
|
dt |
dt |
|
x(0) 0.01
x'(0) 0
x Odesolve(t200)
t 0.1 0.2 200
3
2
1
x(t) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
0 |
50 |
100 |
150 |
200 |
||||||||||
|
|||||||||||||||
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2
3
t
|
|
1 |
|
0 |
.5 |
d x(t) |
3 2 1 0 1 2 3 |
|
dt |
||
|
0 |
.5 |
|
1 |
|
|
|
x(t) |
a 2
k 0.4
Given
d2 |
x(t) k x(t) |
|
a 1 |
x(t)2 d x(t) |
|
|
|||
|
|
|||
2 |
|
|
|
dt |
dt |
|
x(0) 0.01
x'(0) 0
x Odesolve(t200)
t 0.1 0.2 200
3 |
|
|
|
|
2 |
|
|
|
|
1 |
|
|
|
|
x(t) |
|
|
|
|
0 |
50 |
100 |
150 |
200 |
1 |
|
|
|
|
2 |
|
|
|
|
3 |
|
|
|
|
|
|
t |
|
|
|
4 |
|
2 |
d x(t) |
3 2 1 0 1 2 3 |
dt |
|
|
2 |
|
4 |
|
x(t) |
a 0.01
k 0.05
Given
d2 |
x(t) k x(t) |
|
a 1 |
x(t)2 d x(t) |
|
|
|||
|
|
|||
2 |
|
|
|
dt |
dt |
|
x(0) 0.01
x'(0) 0
x Odesolve(t200)
t 0.1 0.2 200
0 |
.0 |
4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.01 |
|
|
|
|
|
|
|||
0 |
.0 |
2 |
|
|
|
|
|
|
|
|
|
|
|
|
d |
|
|
|
|
5 10 3 |
|
|
|
|
|
|
|||||||
x(t) |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
x(t) |
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
0 |
50 |
100 150 |
200 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||||||||
|
|
|
|
|
dt |
0.04 |
0.02 |
0 |
0.02 0.04 |
||||||||||||||||||||||||
|
|
|
|
|
|
||||||||||||||||||||||||||||
|
|
|
|
|
|
|
|||||||||||||||||||||||||||
0 |
.02 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
3 |
|
|
|
|
|
|
||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
5 10 |
|
|
|
|
|
|
|
|||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||||
0 |
.0 |
4 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
0.01 |
|
|
|
|
|
|
||||||
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
t |
x(t) |
|
w 0.8 |
f 1 |
|
r 0.05 |
|
|
|
|
|
|
|
|
|||||
v 4 |
|
b 0.1 |
|
|
|
|
|
|
|
|
|
|
|
|||
Given |
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
d |
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|||||||
|
2 |
|
|
|
|
|
|
|
b |
v |
|
|
|
x(t) |
|
|
|
|
|
|
|
|
|
|
|
||||||||
d |
|
|
x(t) |
r d |
x(t) w2 x(t) |
|
f v |
d x(t) e |
|
|
dt |
|
|
|
||
|
|
|
|
|
|
|
|
|
||||||||
dt2 |
|
dt |
|
|
|
dt |
|
|
|
|
|
|
|
x(0) 0.01
x'(0) 0
x Odesolve(t200)
t 0.1 0.2 200
|
3 |
|
|
|
|
|
2 |
|
|
|
|
x(t) |
2 |
|
|
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|
|
|
1 |
|
|
|
|
|
d x(t) |
|
|
|
|
d x(t) |
|
|
|
|
|
|
|
|
|
||
|
|
|
|
|
dt |
0 |
1 |
2 |
3 |
||
dt |
|
0 |
50 |
100 |
150 |
200 |
1 |
|
|
|
|
|
1 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
2 |
|
|
|
|
|
2 |
|
|
|
|
|
|
|
|
t |
|
|
|
|
|
x(t) |
|
w 8 |
|
f 2 |
|
r 0.05 |
|
|
|
|
|
|
|
|
||||
v 4 |
|
b 0.1 |
|
|
|
|
|
|
|
|
|
|
|
|||
Given |
|
|
|
|
|
|
|
|
|
|
|
|
|
|||
|
|
|
|
|
|
|
|
|
|
|
d |
|
|
|
||
|
|
|
|
|
|
|
|
|
|
|||||||
|
2 |
|
|
|
|
|
|
|
b |
v |
|
|
|
x(t) |
|
|
|
|
|
|
|
|
|
|
|
||||||||
d |
|
|
x(t) |
r d |
x(t) w2 x(t) |
|
f v |
d x(t) e |
|
|
dt |
|
|
|
||
|
|
|
|
|
|
|
|
|
||||||||
dt2 |
|
dt |
|
|
|
dt |
|
|
|
|
|
|
|
x(0) 0.01
x'(0) 0
x Odesolve(t200)
t 0.1 0.2 200
|
0 |
.2 |
|
|
|
|
x(t) |
0 |
.1 |
|
|
|
|
|
|
|
|
|
|
|
d x(t) |
0 |
50 |
100 |
150 |
200 |
|
dt |
0.1 |
|
|
|
|
|
|
|
|
|
|
||
|
0.2 |
|
|
|
|
|
|
|
|
|
t |
|
|
0 |
.2 |
0 |
.1 |
d x(t) |
|
dt |
0.01 0.02 0.03 0.04 0.05 0.06 |
0.1 |
|
0.2 |
|
|
x(t) |