Abstract
The lateral oscillation of a simple levitated body, which is guided by magnetic forces, is examined theoretically and experimentally. Considering the relative vertical motion between the body and the magnetic guides, an ordinary nonlinear differential equation with periodic variable coefficients, which governs lateral oscillations of a simple levitated body, is derived. It is solved by use of the method of multiple scales with respect to time. As the main result, the condition of passing through the parametric resonance, is discussed in the case of primary resonance. It is also shown that a forced oscillation due to the unsymmetry of magnetic guide forces occurs at the same time in the case of secondary parametric resonance. Furthermore, the transient phenomena of passing through the primary resonance have been observed with a simple experimental apparatus. The steady-state oscillations under the combined influence of parametric and external excitations, have been observed in the secondary resonance.
