Harmonic oscillator

  • Thread starter flower76
  • Start date
  • #1
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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?
 

Answers and Replies

  • #2
Doc Al
Mentor
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flower76 said:
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. :grumpy:
 
  • #3
51
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I think I see my error.

Is the answer x = 0.71A ?
 
  • #4
Doc Al
Mentor
45,135
1,433
Yep. [itex]x = (1/\sqrt{2}) A[/itex]
 

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