Dynamic Dipole-Dipole Magnetic Interaction and Nonlinear Damped Oscillations

Haiduke Sarafian

Pennsylvania State University
University College
York, PA 17403

Abstract

We consider a pair of identical permanent cylindrical magnets. In a laboratory setting, we place one of the magnets at the bottom of a vertical glass tube and drop the second magnet in the tube. The mutual repulsive interaction of the magnets along with the other unbalanced forces results a damped nonlinear oscillations.  We characterize the magnets by their masses and magnetic moments; by adjusting the viscosity coefficient we quantify the equation of motion. The equation is a highly nonlinear ODE—we solve the equation numerically. Our theoretical model perfectly matches the data.