= Frequency bandwidth of viscous oscillator power absorption
{title2=$\omega_2-\omega_1=\gamma$}
For a <forced harmonic oscillator> with constant viscous damping coefficient $m\gamma>0$, the <average power> divided by its maximum is $\gamma^2\omega^2/[(\omega_0^2-\omega^2)^2+\gamma^2\omega^2]$. It peaks at $\omega_0=\sqrt{k/m}$. Its two positive half-power <angular frequencies> are $\omega_{1,2}=(\sqrt{4\omega_0^2+\gamma^2}\mp\gamma)/2$. Hence their separation is exactly $\gamma$, and their product is $\omega_0^2$. The narrow-resonance approximation $\omega_{1,2}\simeq\omega_0\mp\gamma/2$ is needed for symmetry about the peak, not for the exact bandwidth in angular-frequency units.
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