For the following transfer function \(T_{\mathrm{V}}(s)=V_{2}(s) / V\) \(1(s)\)

\[
T(s)=\frac{10^{8}(s+100)^{2}}{(s+1000)^{4}}
\]

(a) Use MATLAB to plot the Bode magnitude and phase of the transfer function.

(b) Is this a low-pass, high-pass, bandpass, or bandstop function? Estimate the cutoff frequency(ies) and passband gain.

(c) What is the output \(v_{2}(t)\), if \(v_{1}(t)=20 \cos (1000 t-\) \(\left.45^{\circ}ight) \mathrm{V}\) ? Repeat if \(v_{1}(t)=20 \cos \left(10,000 t+45^{\circ}ight) \mathrm{V}\)