The OP AMP circuit in Figure P10-63 is in the zero state.

(a) Transform the circuit into the \(s\) domain and use the \(\mathrm{OP}\) AMP circuit analysis techniques developed in Section 4-4 to find the network function \(V_{2}(s) / V_{1}(s)\).

(b) Determine the possible purpose of this circuit by testing it at \(s=0\) and \(s=\infty\).

(c) Write the denominator of the network function so that it looks like equation. Select values for the parameters so that \(\omega_{0}=10 \mathrm{krad} / \mathrm{s}\) and \(\zeta=1\).