In an Electrical Circuit, a Damping Force Can Be Provided $L \frac{d^{2} Q}{d t^{2}}+R \frac{d Q}{d t}+\frac{1}{C} Q=0$

question 19

Essay

In an electrical circuit, a damping force can be provided by a resistor.In this case, the differential equation $L \frac{d^{2} Q}{d t^{2}}+R \frac{d Q}{d t}+\frac{1}{C} Q=0$ describes the charge Q on a capacitor in a circuit with inductance L, capacitance C, and resistance R.Suppose L = 1 henry, R = 50 ohms and C = 0.0016 farads.Find a formula for the charge, Q, when $Q(0)=0$ and $Q^{\prime}(0)=2$ .

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