Hi Guys,

I'm having a bit of trouble with a diff equation, I've never dealt with anything quite as complicated as it before and have no idea what to do.

I've been given the equation $\displaystyle m x\prime \prime (t) + b x\prime (t) + k x(t) = 0$, and also the general solution $\displaystyle x(t) = A\cos(\omega t + \varphi)e^{-\alpha t}$

What i have to do is find $\displaystyle \omega\ and\ \varphi$ in terms of k, b and m. I've never dealt with a 2nd order diff equation where x(t) isn't simply $\displaystyle e^{kt}$ so I don't really have a clue what to do. I tried calculating the derivatives of x and substituting them into the diff equation, but i couldn't seem to rearrange the thing to look anything like the general solution of x.

Any help would be greatly appreciated,

Thanks!

EDIT: What i have to do is find $\displaystyle \omega\ and\ \alpha$