If the input to the \(R L C\) circuit of Figure P10-18 is \(v_{\mathrm{S}}(t)\) \(=u(t)\) :

(a) Find the output voltage transform across each element.

(b) Compare the three outputs with regard to their respective poles and zeros.

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