Chapter 4.4, Problem 12P

(a) A series circuit has a capacitor of ${10}^{-5}$ farad, a resistor of $3\times {10}^2$ ohms, and an inductor of $0.2$ henry. The initial charge on the capacitor is ${10}^{-6}$ coulomb and there is no initial current. Find the charge $q$ on the capacitor at any time $t$.

(b) Draw a phase portrait of the equivalent dynamical system that includes the trajectory corresponding to the initial value problem in part (a).