Validity of Small-Loss Approximation

One might ask how accurate are the small-loss approximations leading to (48). We can give a quantitative answer by considering the knee of the curve in Fig. 4, and saying that we are in the small-losses case if the knee is lower than the lowest modal frequency of the resonator. Given a certain value of friction $\Upsilon$, we can find the best approximating IIR filter and then find its knee frequency $\omega_{\mbox{k}}$, corresponding to a magnitude that is $1 + d$ times the asymptotic value, with $d$ a small positive number. If such frequency $\omega_{\mbox{k}}$ is smaller than the lowest modal frequency we can take the small-losses assumption as valid and use the scheme of fig 3.