# Determine unhampered natural frequency and motor constants from graph?

I can find zeta from the PO given in the graph but I don't know any rule relate wn with tp and I don't have value of the of ts and tr

For part b and c I don't know where to start

• I wish for a world where we all have discarded two-phase AC servomotors on a shelf in our parts rooms. – CharlieHanson Dec 9 '15 at 0:42

Time to 1st peak: $t_p =\large\frac{\pi}{\omega _n\sqrt{1-\zeta^2}}$
$\small \pm 2\%$ settling time: $\small T_{S2} \approx \large\frac{4}{\zeta \omega _n}$
$\small 10\%-90\%$ rise time: $t_r \approx\large \frac {1\:+\:1.1\zeta\:+1.4\zeta^2 }{\omega_n}$
Peak overshoot to a unit step input: $\small M_{pt}=1\:+\:\large e^{\small{-\zeta \pi}\large/\small{\sqrt{1-\zeta^2}}}$