Originally Posted by

**CorruptioN** Hi,

I'm working on a 2nd order DE which describes the motion of a damped spring

$\displaystyle mx'' + bx' + kx = 0$

I have found the general solution:

$\displaystyle x(t) = A cos(\omega t + \phi)e^{-\alpha t}$

Where:

$\displaystyle \alpha = b/{2 m}$ and $\displaystyle \omega=\sqrt{k/m - b^2/{4 m^2}}$

which I believe is correct. I now have to find the general solution of $\displaystyle A$ and $\displaystyle \phi$ using $\displaystyle x(0) = x0$ and $\displaystyle x'(0) = v0$. I'm not really sure where to go with this, so could someone point me in the right direction please?

Thanks!