In an oscillating system, a restoring force is a must. In an L-C circuit, restoring force is provided by:

In oscillating system, total energy is always constant. Charge across capacitor and current across inductor is oscillating.When current is maximum, charge on capacitor is zero and all energy is stored in inductor. The current then slowly decreases and charge on the capacitor increases. Hence, here restoring force is provided by the inductor.When charge on capacitor is maximum, current is zero and all energy is stored in capacitor. The current then slowly increases and charge on the capacitor decreases. Hence, here restoring force is provided by the capacitor.