# Harmonic oscillator

by flower76
Tags: harmonic, oscillator
 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?
Mentor
P: 41,449
 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.
 P: 51 I think I see my error. Is the answer x = 0.71A ?
 Mentor P: 41,449 Harmonic oscillator Yep. $x = (1/\sqrt{2}) A$

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