1. The problem statement, all variables and given/known data A simple harmonic oscillator has a total energy E. a) Determine the kinetic and potential energies when the displacement is one half the amplitude. b) For what value of the displacement does the kinetic energy equal the potential energy? 2. Relevant equations PEs= 1/2Kx^2 KE = 1/2mv^2 3. The attempt at a solution I actually have the solution given to me, but I don't understand some of the steps. We know that x=A/2, so: PEs= 1/2K(A/2) which we can expand to K/8A^2 Then they say that: K/8A^2 = K/8(2E/K) and this is the part I'm confused about. Why does A^2=2E/K? Thanks!