Graphics Programs Reference
In-Depth Information
=
where
w
0
is the displacement at
r
a
. Use numerical integration to determine
w
/
w
0
at
r
=
2
a
.
13.
x
m
b
k
The mass
m
is attached to a spring of free length
b
and stiffness
k
. The coefficient
of frictionbetween the mass and the horizontal rodis
µ
. The acceleration of the
mass can be shown to be(you may wish to provethis)
x
=−
f
(
x
), where
x
)
1
k
m
(
b
f
(
x
)
=
µ
g
+
µ
b
+
−
√
b
2
+
x
2
If the mass is released fromrest at
x
=
b
, its speedat
x
=
0 is givenby
2
b
0
v
0
=
f
(
x
)
dx
Compute
v
0
by numerical integrationusing the data
m
=
0
.
8 kg,
b
=
0
.
4 m,
81 m/s
2
.
14.
Debye'sformula for the heatcapacity
C
V
of a solid is
C
V
=
µ
=
0
.
3,
k
=
80N/m and
g
=
9
.
9
Nkg
(
u
), where
u
3
1
/
u
0
x
4
e
x
(
e
x
g
(
u
)
=
1)
2
dx
−
The terms in thisequationare
N
=
number of particles in the solid
k
=
Boltzmann constant
u
=
T
/
D
T
=
absolute temperature
D
=
Debyetemperature
Compute
g
(
u
)from
u
=
0to1
.
0 in intervals of 0
.
05 and plot the results.
15.
Apower spike in an electriccircuit results in the current
i
0
e
−
t
/
t
0
i
(
t
)
=
sin(2
t
/
t
0
)
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