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Harmonic oscillator

by flower76
Tags: harmonic, oscillator
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flower76
#1
May3-06, 02:24 PM
P: 51
Can someone check my work please I'm pretty sure I don't have the right answer but I can't figure out what I have wrong.

The question is:
A simple harmonic oscillator has total energy E=1/2kA^2
where A is the amplitude of oscillation.
For what value of the displacement does the kinetic energy equal the potential energy?

So I figure that if KE is equal to PE, then PE=1/2E

Therefore:

1/2kx^2 =1/2(1/2kA^2)
kx^2 = 1/2kA^2
x = 1/4A

Any ideas?
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Doc Al
#2
May3-06, 02:53 PM
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P: 41,449
Quote Quote by flower76
So I figure that if KE is equal to PE, then PE=1/2E
Good.

Therefore:

1/2kx^2 =1/2(1/2kA^2)
Good.
kx^2 = 1/2kA^2
Good.
x = 1/4A
Not good.
flower76
#3
May3-06, 02:59 PM
P: 51
I think I see my error.

Is the answer x = 0.71A ?

Doc Al
#4
May3-06, 03:01 PM
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P: 41,449
Harmonic oscillator

Yep. [itex]x = (1/\sqrt{2}) A[/itex]


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