This article proposes a novel mean for tuning the natural frequency of an electromagnetic resonant shunt, using a pulse-width modulation (PWM) circuit. It is used to modulate the value of the capacitance of the shunt, and the electrical frequency is shown to be proportional to the command parameter of the PWM, the duty cycle. An easy and efficient strategy to tune the resonant shunt in real time is then proposed, thus obtaining a low powered and always stable vibration control device. The article proposes the theory of PWM, giving a robust method to predict the dynamics of the system. Then, an accurate multi-mode theoretical model of the tunable resonant shunt coupled to an elastic structure is proposed and experimentally validated on an elastic multi-mode structure, in the case of two different control strategies. The first one is a standard resonant shunt with both the electrical frequency and damping optimized to reduce a given resonance peak. The second one is based on a resonant shunt with the electrical damping as low as possible, which creates an antiresonance and a “notch” type mechanical response at the driving frequency. Both strategies are experimentally validated with real time variation and adaptation of the electrical frequency, obtaining an efficient vibration control device, able to reduce by a factor 40 the vibration level.