If the input to the \(R L C\) circuit of Figure \(\mathrm{P}_{10-18}\) is \(v_{\mathrm{S}}(i)=u(t)\) :

(a) Find the output voltage transform \(V_{\mathrm{LC}}(s)\) across \(L\) and \(C\) taken together.

(b) Use the initial- and final-value theorems to determine the value of the voltage across the combined elements at \(t=\) 0 and \(t=\infty\). What conclusions can one draw regarding the results?