Damped spring mass system - parameter estimation
I think I got the answer: I look at the step response of the system.

$H(s) = \frac{1}{ms^2+ds+c}$  

The limit of the step response equals my parameter $1/c$

$y(\infty)=\lim_{s\rightarrow 0} s\cdot \frac{1}{s} \cdot H(s) = \frac{1}{c}$  

Using $c$ and $c/m$ from the measurements above I can calculate the mass $m$. 

I hope this is right, but the results look reasonable...