Department of Physics
Prof. R. Bundschuh
The Ohio State University
Third Problem Set for Physics 664 (Theoretical Mechanics)
Spring quarter 2004
Important dates:
May 31 no class, Jun 9 9:30am11:18am Fnal exam
Due date:
Thursday, Apr 15
7. Anharmonic oscillator
8 points
As another example of an anharmonic oscillator, we will consider a particle of mass
m
that
moves in one dimension under the in±uence of the force
F
(
x
) =

F
0
x

x

=
+
F
0
x <
0
0
x
= 0

F
0
x >
0
a) Calculate the potential
U
(
x
) corresponding to this force with
U
(
x
= 0) = 0.
[Hint:
calculate the potential independently for
x >
0 and
x <
0 and piece your solutions
together afterward.]
b) Derive the relation ˙
x
(
x
) and draw the phase portrait for this anharmonic oscillator.
c) Solve the equation of motion of the anharmonic oscillator for the initial conditions
x
(0) =
A
and ˙
x
(0) = 0 for times
t
during which
x
(
t
)
>
0.
d) Calculate the dependence of the period
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 Fall '04
 BUNDSCHUH
 mechanics, Periodic function, Prof. R. Bundschuh, anharmonic oscillator

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