Interaction Forces in Coupled Magnetic Pendulums

Abstract

In this research, we investigated the non-linear motion and magnetic forces in a chain of magnetic pendulums with cylindrical magnets to eventually better understand the be- haviour of Josephson junction-effect devices. We studied the nonlinear motions of our system through the interaction forces between the magnets and analytically derived the equations of motion with the aim of simulating the dynamics of the system. To obtain the natural frequencies of our analytical system, we used the Fast Fourier transform. Finally, we validated the accuracy of our simulated system’s response by comparing its behaviour to that of an experimental setup consisting of two coupled magnetic pendulums. Ultimately, we solved for the equations of motions of our magnets and integrated the magnetic forces from the magnetic field function. We also experimentally validated the nonlinear response of the system as well as its equilibrium points and natural frequency. The results we obtained through comparing the simulated system response and the de- signed experiment response indicated that our analytical model can accurately predict the behaviour of such a system.