The problem of energy harvesting from a single degree of freedom oscillator is considered. The oscillator comprises a magnetic transducer, providing a damping force which can be modulated in real time. The goal of the control law is to choose such a modulation with the constraint to achieve a periodic evolution (with the same period as the exciting signal) and the objective to maximize the amount of energy extracted during each period. The application of the Pontryagin Maximum Principle shows that the optimal strategy can contain both regular phases (during which the modulated damping is either at its maximum or its minimum value) and singular phases (during which the optimal choice of damping has smooth variations). Such a phenomenon is markedly different in optimal energy harvesting with respect to optimal energy dissipation and time optimal vibration damping, where the optimal strategy is a bang-bang feedback (that is, operating at either minimum or maximum damping).