Find the transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V_{1}(s\) ) for the circuit in Figure P12-45 .
(a) Use MATLAB to generate a Bode plot of your transfer function. From the Bode plots, estimate the amplitude and phase of the steady-state output for each of the following input signals
\[
\begin{gathered}
v_{1}(t)=10 \cos 10 t \mathrm{~V}, \\
v_{1}(t)=10 \cos 100 t \mathrm{~V}, \text { and } \\
v_{1}(t)=10 \cos 1000 t \mathrm{~V} .
\end{gathered}
\]

(b) calculate the actual output amplitude and phase for these three inputs and compare the results with your estimates.

(1) 1 F 100 V(1)