Damped Harmonic Motion (Physics)

This is a physics related question involving some calculus.

I have made numerous attempts trying different strategies, but to no avail. I am not sure how to set up this problem. Each time I try to solve for b, I get an equation that is "impossible" to solve (according to Mathematica 7).

Can someone please explain how to approach this problem?

Relevant (possibly) equations:

$\displaystyle

x = Ae^{(-b/2m)t}cos\omega't

$

$\displaystyle

\omega' = \sqrt{\frac{k}{m} - \frac{b^2}{4m^2}}

$

$\displaystyle m\frac{d^2x}{dt^2} + b\frac{dx}{dt} + kx = 0$

Thanks,

Patrick