The question is: what fraction of thetotal energy of a simple harmonic oscillato

Question

The question is: what fraction of thetotal energy of a simple harmonic oscillator is kinetic and whatfraction potential when the displacement is 1/3 the maximumamplitude. I solved for potential energy, but I can't figure outhow to solve for KE

Using E = 1/2kA2 and the fact that A = 3x:
E = 1/2k(3x)2 so E = 9(1/2kx2) so totalenergy is 9 times the PE How do I solve for kinetic energy? The question is: what fraction of thetotal energy of a simple harmonic oscillator is kinetic and whatfraction potential when the displacement is 1/3 the maximumamplitude. I solved for potential energy, but I can't figure outhow to solve for KE

Using E = 1/2kA2 and the fact that A = 3x:
E = 1/2k(3x)2 so E = 9(1/2kx2) so totalenergy is 9 times the PE How do I solve for kinetic energy? How do I solve for kinetic energy?

Explanation / Answer

Kinetic energy K = ( 1/ 2) m w ^ 2 [ A ^ 2 - x ^ 2] Total energy E = ( 1/ 2) m w ^ 2 A ^ 2 Required fraction K / E = [ A ^ 2 - x ^ 2 ] / A ^2 Given displacement x = A /3 sibstitute values we get K / E = [ A ^ 2 - ( A / 3 ) ^ 2] / A ^ 2                                             = [ (8 A ^ 2) / 9 ] / A ^ 2                                             = 8 / 9

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