Average energy of a damped driven oscillator

[Bestphysics112]

Homework Statement

http://imgur.com/a/lv6Uo

Homework Equations

Look below

The Attempt at a Solution

I was unsure where to start. I thought that parseval's theorem may be helpful. I know the Potential energy is equivalent to .5kx^2 and T will be the integral of the force. So i have $$<E> = \frac{1}{t} \int_{-t/2}^{t/2}\frac{1}{2}kx^2dt + \frac{1}{t}\int_{-t/2}^{t/2}\sum_{n=1}^{\infty} f_0_n cos(nwt+\phi_n)dt$$

Is this on the right track? If it is, how can i simplify this?

Edit: I can't figure out how to use latex so here is my work so far: http://imgur.com/a/eTigf

 

[Bestphysics112]

After re reading my textbook I was able to get the correct answer