Question

Calculate the ratio of the kinetic energy to the potential energy of a simple harmonic oscillator when its displacement is half its amplitude.

Wouldn't it just be K/U=1/1 or just 1
Because at half the amplitude, it's going to be a combination of K and U. At one extreme all the energy will be kinetic, and at the other extreme all energy will be potential. Therefore halfway between they must equal each other for a 1:1 ratio... right?
bobpursley
PE= 1/2 kx^2
KE= 1/2 m v^2

put in the expression for v in terms of x

find each when x=1/2 Amplitude.

You will then find the answer, and it is not your guess above.

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