Combination resonance of a magnet over a high-T_c superconductor excited vertically

This research deals with nonlinear dynamics of a permanent magnet freely levitated above a high-T_c superconductor(HTSC) excited in the vertical direction. Magnetic force and torque can be evaluated analytically by the advanced mirror image method as nonlinear functions of both displacement and roll angle of the magnet. Equations of 3 d.o.f. motion show that the magnet has two oscillation modes due to linear coupling of the horizontal and roll motions. The both modes can be excited by nonlinear coupling with vertical motion when the superconductor is exited vertically in the neighborhood of the sum of the natural frequency of each mode. Frequency response of this combination resonance was numerically simulated. This resonance was also observed in experiments.