New Jersey Institute of Technology

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A series circuit has an inductor of 0.5 henry, a resistor of
2 hms and a capacitor of 0.05 farad. The initial charge on the capacitor is zero and the initial current is 1 A. A voltage source of $E(t)=3 \cos 2 t$ volts is analogous to an external force. Find the charge on the capacitor and the current at any time $t$.