The \(R L C\) circuit in Figure \(\mathrm{P}_{9}=45\) is in the zero state when at \(t=0\) an exponential source, \(v_{\mathrm{S}}(t)=V_{\mathrm{A}} e^{-\alpha t} \mathrm{~V}\), is suddenly connected to it.

(a) Find the circuit integrodifferential equation that describes the behavior of the current in the circuit.

(b) If \(R=68 \Omega, L=100 \mathrm{mH}, C=15 \mu \mathrm{F}, V_{\mathrm{A}}=15 \mathrm{~V}\), and \(\alpha=\) \(100 \mathrm{~s}^{-1}\), use Laplace transforms and MATLAB to solve for \(i\) ( \(t\) ) for \(t \geq 0\).