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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