Kirchhoff’s voltage law states that the sum of the voltage dropsacross a resistor, R, an inductor, L, and a capacitor, C, in anelectrical circuit must be the same as the voltage source, E(t),applied to that RLC circuit. Applying the additional fact that thecurrent, I, is related to the charge, q, by the relationshipI=dq/dt, the resulting ODE model for the charge in a circuit is: L(d^2 q)/(dt^2 )+R dq/dt+1/C q=E(t). If a 100 sin?(60t)source isconnected to an RLC circuit with a 1/20 henry inductor, L, a 1 ohmresistor, R , and a 1/130 farad capacitor, C, find the charge q(t)given that q(0)=0 and I(0)=q'(0)=0.
