LRC-Circuit II: A series LRC-circuit with no input voltage has a resistor of 15 ohms, an inductor of 1 henry, and a capacitor of 0.02 farads. Initially, the charge on the capacitor is 5 coulombs, and there is no current.
(a) Determine the IVP for the charge across the capacitor.
(b) Solve the IVP in (a) for the charge across the capacitor for t > 0.
(c) Determine the current in the circuit for t > 0.
(d) What are the long-term values of the charge and current?