In a series \(R L C\) circuit, the step response across the 1\(\mu \mathrm{F}\) capacitor is

\[
v_{\mathrm{C}}(t)=25-e^{-400 t}[15 \cos (1000 t)+3 \sin (1000 t)] \mathrm{V} \quad t \geq 0
\]

(a) Find \(R\) and \(L\).

(b) Find \(i_{\mathrm{L}}(t)\) for \(t \geq 0\).