Critical galvanometer transfer function

With $e^{i\omega t}$ phasors, critical damping gives $\Theta (\omega )=F_0/({\omega }_0+i\omega {)}^2$, amplitude $F_0/({\omega }_0^2+{\omega }^2)$ and phase $-2\arctan (\omega /{\omega }_0)$. The response strongly suppresses alternating currents well above the mechanical frequency.