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 Kirchhoff's Laws give the following 2nd order differential equation for Q(t): L Q00 (t) + R Q0 (t) + 1 Q(t) = E(t) C () R E(t) L C Questions: Assume L = 1, C = 1/5, R = 4 and E(t) = 10 cos t. 1. Use ode45 (and plot routines) to plot the solution of () with Q(0) = 0 and Q0 (0) = 0 over the interval 0 t 80 for = 0, 0.5, 1, 2, 4, 8, 16. 2. Let A() = maximum of |Q(t)| over the interval 30 t 80 (this approximates the amplitude of the steady-stat solution). Experiment with various values of and discuss what appears to happen to A() as and as 0. Also, interpret your findings in terms of an equivalent spring-mass system. Remark: There is an analogy between spring-mass system and RLC circuits given by: Spring-mass system m u00 + c u0 + k u = F (t) RLC circuit L Q00 + R Q0 + 1 C Q = E(t) u = Displacement Q = Charge u0 = Velocity Q0 = I = Current m = Mass L = Inductance c = Damping constant R = Resistance k = Spring constant 1/C = (Capacitance)1 F (t) = External force E(t) = Voltage