A high-stiffness stabilizer/bearings for passive magnetic bearing systems is provide where the key to its operation resides in the fact that when the frequency of variation of the repelling forces of the periodic magnet array is large compared to the reciprocal of the growth time of the unstable motion, the rotating system will feel only the time-averaged value of the force. When the time-averaged value of the force is radially repelling by the choice of the geometry of the periodic magnet array, the Earnshaw-related unstable hit motion that would occur at zero rotational speed is suppressed when the system is rotating at operating speeds.