Ringdown ($x(t)=A{e}^{-\gamma t}\cos (\nu t+\varphi )$)

Ringdown is the freely decaying motion of a resonator after an applied drive is removed. For an underdamped damped harmonic oscillator, the amplitude decays as $e^{-\gamma t}$ while the angular frequency is $\nu =\sqrt{{\Omega }^2-{\gamma }^2}$. In the weak-damping limit, the cycle-averaged stored energy decays as $e^{-2\gamma t}$, giving the quality factor from ringdown $Q\simeq \Omega /(2\gamma )$.