Exercise

An RLC circuit may be modeled by the differential equation LI''+RI'+(1/C)I=E(t), where L is the inductance, R is the resistance, C is capacitance, I(t) is current at time t, and E(t) is a voltage source.

Let R=100 ohms, L=10 henrys, C=1/100 farads, and let E(t) be the periodic extension of

100t(Pi^2-t^2) -Pi<=t<=Pi (in volts). Find the steady state current (t->infinity) in such a circuit. Follow the example given above:

Plot two periods of E(t), develop a Fourier series for E(t), do undetermined coefficients, and get the first few terms of the steady state solution. Plot this.

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