Chapter 16.3, Problem 30E

Electrical Circuits

In Exercises 29 and 30, use the electrical circuit differential equation

$\frac{d^{2}q}{d{t}^2}+\left(\frac{R}{L}\right)\frac{dq}{dt}+\left(\frac{1}{LC}\right)q=\left(\frac{1}{L}\right)E\left(t\right)$

where R is the resistance (in ohms), C is the capacitance (in farads), L is the inductance (in henrys), E(t) is the electromotive force (in volts), and q is the charge on the capacitor (in coulombs). Find the charge q as a function of time t for the electrical circuit described. Assume that $q\left(0\right)=0$ and $q\text{'}\left(0\right)=0$.

$R=20,C=0.02,L=1,E\left(t\right)=10\sin 5t$