Elastic Potential Energy and SMH

[Roze]

Homework Statement

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?

Homework Equations

PEs= 1/2Kx^2
KE = 1/2mv^2

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!

 

[Doc Al]

Hint: Express the total energy (E) in terms of amplitude. (At what point is the energy purely PE?)

 

[Roze]

When x=0?

 

[Doc Al]

When x=0?

What's the PE when x = 0?