Graphics Programs Reference
In-Depth Information
9.
Solve the stiff problem—see Eq. (7.16)
y
+
1001
y
+
y
(0)
1000
y
=
0
y
(0)
=
1
=
0
2with the adaptive Runge-Kuttamethod and plot
y
vs.
x
.
from
x
=
0to0
.
10.
Solve
√
2
y
+
2
y
+
y
(0)
3
y
=
0
y
(0)
=
0
=
with the ada
pt
ive Runge-Kuttamethod from
x
=
0to5 (the analytical solutionis
e
−
x
sin
√
2
x
).
11.
Use the adaptive Runge-Kuttamethod to solve the differentialequation
y
=
y
=
2
yy
1,
y
(0)
from
x
=
0to10 with the initialconditions
y
(0)
=
=−
1. Plot
y
vs.
x
.
0,
y
(0)
12.
RepeatProb. 11with the initialconditions
y
(0)
=
=
1and the integration
range
x
=
0to1
.
5.
13.
Use the adaptive Runge-Kuttamethod to integrate
9
y
−
y
x
y
=
y
(0)
=
5
0to5 and plot
y
vs.
x
.
14.SolveProb. 13 with the Bulirsch-Stoermethodusing
H
from
x
=
=
0
.
5.
15.
Integrate
x
2
y
+
xy
+
y
(1)
y
=
0
y
(1)
=
0
=−
2
1 to 20, and plot
y
and
y
vs.
x
. Use the Bulirsch-Stoermethod.
from
x
=
16.
x
m
k
The magnetizedironblock of mass
m
is attached to a spring of stiffness
k
and
free length
L
. The block is at rest at
x
=
L
when the electromagnet isturned on,
x
2
on the block. The differentialequation of
exerting the repulsiveforce
F
=
c
/
the resulting motionis
c
x
2
mx
=
−
k
(
x
−
L
)
Determine the amplitude and the period of the motion by numerical integration
with the adaptive Runge-Kuttamethod. Use
c
=
·
m
2
,
k
=
=
.
5 N
120N/m,
L
0
2m
and
m
=
1
.
0kg.
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