A capacitor is charged to a potential difference of V_o by connecting it across a battery and then is allowed to discharge through an inductor of inductance L.

In starting charge on the plates of the capacitor q_o = CV_o

At any instant, let the charge flown through the circuit be q and the current in the circuit be i. operating Kirchhoff's law

The charge q on the plates of the capacitor and current I in the circuit vary sinusoidally as q = q₀ sin (wt + f)  and  I = q₀ w cos (wt + f).   where f is the initial phase and it depends on initial conditions of the circuit and w = 1/√LC.

            The net power of the system remains conserved

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