The Dynamical Behavior of a Levitated Body with Magnetic Guides : Parametrically Excitation of the Subharmonic Type due to the Vertical Motion of the Levitated Body

Abstract

The nonlinear oscillations of a levitated body, which is moved in a horizontal plane and is guided by magnetic forces on both sides, are examined theoretically and experimentally. The magnetic forces acting on the body are calculated exactly by applying Coulomb's law over and infinitely small area of magnets, and by integrating about four magnetic poles of two magnetic plates. The parametrically excited oscillations of the body, due to the relative vertical motion between the body and the magnetic guides, are studied theoretically by using the above magnetic forces. Also the experiments are preformed with a simple experimental apparatus. As the main results, the oscillation with a fractional-harmonic pair as predicted by the theory, is shown experimentally in the special case when two natural frequencies of the body are nearly commensurable.