Question

At what displacement from the equilibrium is the total energy of a simple harmonic oscillator one - sixths KE and five - sixth PE? Answer should be in terms of the amplitude A.

Answer 1

Let A be the full amplitude displacement and k be the sping constant.

The maximum total energy is
Et = (1/2) k A^2
The potential energy for other displacements is
Ep = (1/2) k x^2

Ep/Et = 5/6 when (x/A)^2 = 5/6
x/A = 0.91287