Motion analysis of magnetic spring pendulum

Abstract In order to analyze the motion characteristics of spring pendulum under the action of magnetic force, the motion of spring pendulum after applying a uniform magnetic field in a straight direction is considered. The first order approximate solution is given by studying the micro-vibration near the equilibrium point. The approximate solutions similar to Foucault's pendulum are also obtained considering the large weight of the pendulum ball and the soft spring. Then, a new internal resonance phenomenon of magnetic spring pendulum is found by harmonic balance method, and the conclusion is that the energy is transmitted in three modes of respiration, swing and deflection in sequence. Finally, the influence of magnetic field on the stability of spring pendulum is investigated, and the bifurcation phenomenon at its equilibrium point is found.