There is no initial energy stored in the circuit in Figure P10-41.
(a) Transform the circuit into the \(s\) domain and formulate node-voltage equations.
(b) Show that the solution of these equations for \(V_{2}(s)\) in symbolic form is

(c) Identify the natural and forced poles of \(V_{2}(s)\).
(d) Find \(v_{2}(t)\) for \(v_{1}(t)=2 u(t) \mathrm{V}, R_{1}=R_{2}=1 \mathrm{k} \Omega, L=\) \(0.1 \mathrm{H}\), and \(C=1 \mu \mathrm{F}\).

Transcribed Image Text:

V(s) = RV (s) (R + R)LC s + (R RC + L)s + R