# Energy of SHM

1. Dec 20, 2006

### mbrmbrg

1. The problem statement, all variables and given/known data

(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?

2. Relevant equations

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

$$K+U=E$$

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

3. 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

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

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

Last edited: Dec 20, 2006
2. Dec 20, 2006

### neutrino

That's correct, and so is -xm/sqrt(2), since the question asked for displacement.

How did you enter the answer? Maybe it was expecting the answer in some other format.

3. Dec 20, 2006

### mbrmbrg

Thanks; that was it. I entered xm/sqrt2, but they wanted xm/sqrt(2). Looks the same when you click the eyeball to ask what it'll look like!