Chapter D2.5, Problem 19E

Analyzing circuit equations Consider the circuit equation

     ${v^{″}}_{\text{out}}+\frac{R}{L}{v^{\prime }}_{\text{out}}+\frac{1}{LC}{v}_{\text{out}}=\frac{1}{LC}{v}_{\text{in}}=\frac{1}{LC}f{e}^{i\omega t}$.

a.    For the given parameter values, compute the gain function.

b.    Graph the gain function and find the location of its maximum value for ω ≥ 0.

c.    On what interval is the gain function monotonically decreasing?

d.    Compute and graph the ratio $\left|\frac{v_{\text{out}}}{v_{\text{in}}}\right|$ and interpret the result.

19.    L = 8, C = 1/120, R = 400