An electrical power generator comprising a first part arranged for reciprocating movement in relation to a second part, wherein: the first part comprises at least one first annular magnet, the magnet comprising a north pole end and a south pole end arranged opposite each other in an axial direction; the second part comprises a core of ferromagnetic material positioned radially inside the first annular magnet, the core comprising a central portion extending in the axial direction, a first radially extending portion and a second radially extending portion, the radially extending portions (22, 23) extending radially from the central portion at two different axial positions, so that the radially extending portions (22, 23) are spaced from each other by a gap extending in the axial direction and surrounding the central portion; the second part further comprises at least one coil wound around the central portion between the radially extending portions (22, 23); the first part being arranged displaceable in a radial direction perpendicular to the axial direction, so that when subjected to a repetitive oscillatory movement in the radial direction, during one cycle of the oscillatory movement: - at one moment of the cycle, a first segment of the first annular magnet will enter the gap whereas a second segment of the first annular magnet will be displaced away from the gap, the second segment being positioned diametrically opposite the first segment, and - at another moment of the cycle, the second segment will enter the gap, whereas the first segment will be displaced away from the gap. the first part comprises at least one first annular magnet, the magnet comprising a north pole end and a south pole end arranged opposite each other in an axial direction; the second part comprises a core of ferromagnetic material positioned radially inside the first annular magnet, the core comprising a central portion extending in the axial direction, a first radially extending portion and a second radially extending portion, the radially extending portions (22, 23) extending radially from the central portion at two different axial positions, so that the radially extending portions (22, 23) are spaced from each other by a gap extending in the axial direction and surrounding the central portion; the second part further comprises at least one coil wound around the central portion between the radially extending portions (22, 23); the first part being arranged displaceable in a radial direction perpendicular to the axial direction, so that when subjected to a repetitive oscillatory movement in the radial direction, during one cycle of the oscillatory movement: - at one moment of the cycle, a first segment of the first annular magnet will enter the gap whereas a second segment of the first annular magnet will be displaced away from the gap, the second segment being positioned diametrically opposite the first segment, and - at another moment of the cycle, the second segment will enter the gap, whereas the first segment will be displaced away from the gap. - at one moment of the cycle, a first segment of the first annular magnet will enter the gap whereas a second segment of the first annular magnet will be displaced away from the gap, the second segment being positioned diametrically opposite the first segment, and - at another moment of the cycle, the second segment will enter the gap, whereas the first segment will be displaced away from the gap.