Near-resonant mechanical susceptibility
= Near-resonant mechanical susceptibility
{title2=$R\simeq[2m\omega_0(-\delta+i\gamma)]^{-1}$}
For the convention $x=\operatorname{Im}(RFe^{i\omega t})$, <viscous damping> $b$ gives $R=[m(\omega_0^2-\omega^2)+ib\omega]^{-1}$. Put $\delta=\omega-\omega_0$ and $\gamma=b/(2m)$. If both are small relative to $\omega_0$, the displayed approximation follows. Its squared modulus has half-width $\gamma$, and the displacement lags the force by $\pi/2$ at $\omega=\omega_0$.