Show that n the free oscillations of an LC circuit, the sum of energies stored in the capacitor and and the inductor is constant in time.

Explanation

To show that in the free oscillations of an LC circuit, the sum of energies stored in the capacitor and the inductor is constant in time, we can follow these steps:

### Step 1: Define the energies stored in the capacitor and inductor
The energy stored in the capacitor \( E_C \) is given by the formula:
\[ E_C = \frac{q^2}{2C} \]
where \( q \) is the charge on the capacitor and \( C \) is the capacitance.
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