Abstract
Parametric resonance occurs in systems with nonlinear restoring force and sinusoidal excitation whose frequency is in the neighborhood of twice that of the systems. The unstable region of the parametric resonance changes according to magnitude of the quadratic nonlinear restoring force. We consider a system subjected to magnetically levitated force which is sinusoidally changed and analyze the nonlinear dynamics by using the method of multiple scales. Magnitude of the quadratic nonlinearity depends on the asymmetry in dimension of magnets and results in the change of the unstable region. Also, we experimentally confirm the theoretical result by a simple experimental apparatus.
