Originally Posted by

**topsquark** This cannot be analytically solved for t. The equation with which I am more familiar with:

$\displaystyle \displaystyle mx^{\prime \prime} + b x^{\prime} + kx = 0$

has, for a standard solution:

$\displaystyle \displaystyle x(t) = A e^{-bt/(2m)}~cos( \omega t + \delta)$

cannot, in general, be solved for t either.

You're stuck with numerical methods for this one, I'm afraid.

-Dan

Come to think of it, my form and yours are essentially the same. All you need to do is expand the cosine in mine and you get your form.