= Displacement-resonance threshold of a viscous oscillator
{title2=$Q>1/\sqrt2$}
Minimizing $(\omega_0^2-\omega^2)^2+4\beta^2\omega^2$ gives a displacement maximum at $\sqrt{\omega_0^2-2\beta^2}$ only when $\beta<\omega_0/\sqrt2$. An underdamped oscillator with $1/2<Q\leq1/\sqrt2$ consequently has no nonzero-frequency displacement peak. The absorbed-power response instead peaks at $\omega_0$, with exact half-power bandwidth $2\beta$ for this model. Comparing bandwidth definitions requires naming the measured response.
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