In this paper we present a novel concept to efficiently harvest vibrational energy at low frequencies and very small displacement. We describe and evaluate an electromagnetic energy harvester which generates power from a magnetic circuit with motion induced variations of an air gap. External vibrations induce oscillations of the gap length around an equilibrium point, due to a linear spring counteracting the magnetic force. The relative position of the spring can be adjusted to optimize the harvester output for excitation amplitude and frequency. A simulation model is built in COMSOL and verified by comparison with lab measurements. The simulation model is used to determine the potential performance of the proposed concept under both harmonic and non-harmonic excitation. Under harmonic excitation, we achieve a simulated RMS load power of 26.5 μW at 22 Hz and 0.028 g acceleration amplitude. From a set of comparable EH we achieve the highest theoretical power metric of 1712.2 µW/cm3/g2 while maintaining the largest relative bandwidth of 81.8%. Using measured non-harmonic vibration data, with a mean acceleration of 0.039 g, resulted in a mean power of 52 μW. Moreover, the simplicity and robustness of our design makes it a competitive alternative for use in practical situations.