When an inductor is oscillated at it's resonant frequency it becomes a parallel LC circuit (Tank circuit). At this frequency the circuit has a theoretical infinite impedance. However, due to the resistance of the inductor energy is dissipated. The power supply provides a small current (equal to the energy dissipated in the tank circuit) to try and keep the tank circuit charged. If the circuit were suddenly switched off the parallel tank circuit would continue to oscillate (between L and C) for a time until all the energy was dissipated. But, wouldn't the inductor also resist the sudden change in current from the power supply and induce a voltage across it equal to V=Lx di/dt?