In a series RLC circuit the zero-input voltage across the 1-F capacitor is Ct = 10e 1000t

In a series RLC circuit the zero-input voltage across the 1-μF capacitor is

υCðtÞ = 10e^−1000tsin 2000t V t ≥ 0

(a) Find the circuit characteristic equation.

(b) Find R and L.

(c) Find iLðtÞ for t ≥ 0.

(d) Find the initial values of the state variables.