 Critical step response of a galvanometer

For $\ddot{\theta }+2{\omega }_0\dot{\theta }+{\omega }_0^2\theta =F$ switched on from rest, $\theta (t)=(F/{\omega }_0^2)[1-(1+{\omega }_{0}t)e^{-{\omega }_{0}t}]$. critical damping is the fastest nonoscillatory step response at fixed natural frequency within the ordinary second-order model.