In an electrical circuit, a capacitor is placed in parallel with an inductor and a switch in series. initially, the switch is open, and the capacitor has a charge q0. the switch is then closed, and the changes in the system are observed. it turns out that the equation describing the subsequent changes in charge, current, and voltage is very similar to that of simple harmonic motion, studied in mechanics. to obtain this equation, we will use the law of conservation of energy. initially, the entire energy of the system is stored in the capacitor. when the circuit is closed, the capacitor begins to discharge through the inductor. as the charge of the capacitor decreases, so does its energy. on the other hand, as the current through the inductor increases, so does the energy stored in the inductor. assuming no heat loss and no emission of electromagnetic waves, energy is conserved, and at any point in time, the sum of the energy stored in the capacitor uc and the energy stored in the inductor ul is a constant u. u=uc+ul=(q^2)/(2c)+(li^2)/2,where q is the charge on the capacitor and i is the current through the inductor ( q and i are functions of time, of course). for this problem, take clockwise current to be positive.