SHM: Half Energy at Displacement

[mbrmbrg]

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

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

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

 

[neutrino]

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

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

 

[mbrmbrg]

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

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!