This research deals with a kind of parametric excitation of a permanent magnet freely levitated above a high-Tc superconductor excited in the vertical direction. We find the magnet has two vibration modes of linearly coupled horizontal translation and roll motion. These two modes are coupled nonlinearly with the vertical motion by the magnetic force and torque. Through nonlinear analysis and numerical simulation, this research discusses parametric resonance of each mode caused by vertical excitation at the frequency in the neighborhood of twice the natural frequency of that mode. Analytical and numerical results show qualitative agreement with experimental ones.
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