How do free electromagnetic oscillations occur in the circuit?

At the moment the coil is connected to a charged capacitor, an electric current arises in it. With an increase in the current in the coil, a self-induction current of the opposite direction arises in it, so the current in the coil increases gradually. It reaches its maximum value when the capacitor is completely discharged. After the capacitor is discharged, the self-induction current in the coil is directed in the same way as before the start of the current decrease. This current charges the capacitor, but the signs of the charges on its plates turn out to be opposite to the original signs. When the self-induction current becomes zero, the capacitor begins to discharge, creating an opposite current in the coil. The capacitor charging and discharging processes are periodically repeated.

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