Computer Project 2. RLC Circuits Goal: Investigate the charge on a capacitor in an RLC circuit with varying voltage. Tools needed: ode45, plot Description: If Q(t) = charge on a capacitor at time t in an RLC' circuit (with R, L and C being the resistance, inductance and capacitance, respectively) and E(t) = applied voltage, then Kirchhoif's Laws give the following 2\" order differential equation for 6205): 1 L Q\"(t) + RQ'OE) + 5 6203) = EU?) (*) R E(t) L 0 Questions: Assume L = 1, C = 1/5, R = 4 and E(t) = 10coswt. 1. Use ode-45 (and plot routines) to plot the solution of (*) with (2(0) = 0 and Q'(0) = 0 over the interval 0 S t S 80 for w = 0,0.5, 1,2,4,8, 16. 2. Let A(w) = maximum of |Q(t)| over the interval 30 g t S 80 (this approximates the amplitude of the steadystat solution). Experiment with various values of w and discuss what appears to happen to A(w) as w > 00 and as w > 0. Also, interpret your ndings in terms of an equivalent springmass system