Repeat Problem 10-32 when \(i_{\mathrm{S}}(t)=10\) sin \(1000 t u(t) \mathrm{mA}\).

Data From Problem 10-32

There is no energy stored in the capacitor in Figure P1032 at \(t=0\). Transform the circuit into the \(s\) domain and use current division to find \(v_{\mathrm{O}}(t)\) when the input is \(i_{\mathrm{S}}(t)=10 e\) \({ }^{-500 t} u(t) \mathrm{mA}\). Identify the forced and natural poles in \(V_{\mathrm{O}}(s)\).