# Energy of SHM

## Homework Statement

(a) When the displacement in SHM is one-half the amplitude xm, what fraction of the total energy is kinetic energy?

(b) What fraction is potential energy?

(c) At what displacement, in terms of the amplitude, is the energy of the system half kinetic energy and half potential energy?

## Homework Equations

$$U=\frac{1}{2}kx^2$$

$$K+U=E$$

$$E=\frac{1}{2}kx_m^2$$

## The Attempt at a Solution

I got parts (a) and (b) quite neatly, and I'm convinced that I got (c) also, only WebAssign isn't so convinced.

WORK FOR PART C:
$$U=\frac{1}{2}E$$

$$\frac{1}{2}kx^2=\frac{1}{2}(\frac{1}{2}kx_m^2)$$

some halfs and k's cancel, leaving

$$x^2=\frac{1}{2}x_m^2$$

$$x=\frac{x_m}{\sqrt{2}}$$

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