If an inductor current is 0 for tlt;0 while capacitor is being charged (the switch is on the capacitor side). when for t0 the capacitor is fully charged and switch moves in such a position that both capacitor and inductor are now connected in series. Will the capacitor charge the inductor? what will be the current in inductor for t0?
If the closing of the switch connects the inductor and capacitor in series into a closed circuit, then the capacitor will discharge through the inductor which will store the energy in its magnetic field. Then the inductor will transfer this stored energy back to the capacitor which will become charged with the opposite polarity (storing the energy in its electric field) and then discharge again in the opposite direction through the inductor. This swinging back and forth of the stored energy between inductor and capacitor will continue indefinitely. With resistance in the circuit (and in practice there is always some) the swings will gradually die out. The undamped swing frequency 2π/√(LC).