= Ringdown comparison bound for two resonator modes
{title2=$Q_1<\omega_1/[\omega_2/Q_2+\ln R_0/t]$}
For two weakly damped <normal modes> with initial <intensity> ratio $R_0>1$, independent exponential <energy> decay gives $I_1(t)/I_2(t)=R_0e^{-t(\omega_1/Q_1-\omega_2/Q_2)}$. An observed reversal to a ratio below one implies the displayed upper bound on $Q_1$, provided the denominator is positive. A strict <intensity> comparison does not determine a unique <quality factor>; equality fixes only the crossing threshold.
Back to article page
