Solve for Displacement in Harmonic Oscillator

AI Thread Summary
The discussion revolves around solving for the displacement in a simple harmonic oscillator where the kinetic energy equals the potential energy. The user initially calculates that the displacement x is equal to 1/4A, but later realizes this is incorrect. The correct displacement, where kinetic energy equals potential energy, is determined to be x = (1/√2)A, which is approximately 0.71A. The error was identified in the final calculation step. The correct understanding of energy distribution in harmonic motion is crucial for accurate results.
flower76
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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?
 
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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.
 
I think I see my error.

Is the answer x = 0.71A ?
 
Yep. x = (1/\sqrt{2}) A
 
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