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(Solved): Problem 4 (RLC Circuit with a Switch) Consider the following circuit, which includes a resistor, cap ...
Problem 4 (RLC Circuit with a Switch) Consider the following circuit, which includes a resistor, capacitor, and an inductor. The battery can provide a constant voltage to this circuit, but it is connected to a switch that can flip on and off. The differential equation that governs the amount of charge on the capacitor is given by:
L(d^(2)Q)/(dt^(2)) R(dQ)/(dt) (1)/(C)Q=E(t)Where the voltage on the battery is given by the following discontinuous function:
E(t)={(3,05):}Assume the following values for the circuit parameters:
L=1,R=13, and
C=(1)/(40). You may also assume the circuit starts from rest and (
:Q^(')(0)=0