# X=xoe^-(bwt)*(cos(wt)+b/(sqrt(1-b)sin(wt)). units of x is mm, t in s. What are the units of w and b?

$b$ is dimensionless. The units of $w$ are $\frac{1}{s}$
${x}_{0} {e}^{-} \left(b w t\right) \cdot \left(\cos \left(w t\right) + \frac{b}{\sqrt{1 - b}} \sin \left(w t\right)\right)$
the arguments of functions like $\sin$, $\cos$, $\exp$ have to be dimensionless.