# Harmonic oscillator

1. ### flower76

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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### Staff: Mentor

Good.

Good.
Good.
Not good. :grumpy:

4. ### flower76

51
I think I see my error.

Is the answer x = 0.71A ?

### Staff: Mentor

Yep. $x = (1/\sqrt{2}) A$