The transfer function for a second-order LPF with \(T_{\max }=\mathrm{OdB}\) is

\[
T_{\mathrm{V}}(s)=\frac{\omega_{0}^{2}}{s^{2}+2 \zeta \omega_{0} s+\omega_{0}^{2}}
\]

Find the location of the poles that will cause the cutoff frequency \(\omega\) \({ }_{\mathrm{C}}\) to equal the resonant frequency \(\omega_{0}\). Then for those poles find \(\zeta\) and Q. One might be tempted to set \(2 \zeta \omega_{0}=B=\omega_{0}\) and hence \(\zeta=\) 0.5 ; however, this is not the case. Verify your result using MATLAB; select \(\omega_{0}=10^{4} \mathrm{rad} / \mathrm{s}\).