https://doi.org/10.1140/epjp/s13360-023-03882-w
Regular Article
Dynamic analysis of magnetic spring pendulum in viscous media
Wanjiang College, Anhui Normal University, Wenjin West Road, 241003, Wuhu, Anhui, China
Received:
4
November
2022
Accepted:
9
March
2023
Published online:
7
April
2023
In order to explore the motion law of the spring pendulum under the action of magnetic field force in a viscous medium, firstly, the system of dynamic equations of the system is linearized, and two types of approximate solutions are obtained. From this approximate solution, it can be shown that the motion state of the system is similar to the superposition of the damping Foucault pendulum motion in the 
plane with the damping vibration in the Z direction. At the same time, the approximate solution expressions under different initial conditions are analyzed and summarized in detail, and it is found that the motion forms on the plane are divided into hypocycloid, rose curve, and rotating ellipses with gradually decreasing motion amplitude. Then, through the mechanical resonance conditions, the new internal resonance relationship of the magnetic spring pendulum is obtained, and then, it is found that its energy is transmitted in the three modes of respiration, oscillation, and deflection in sequential order. In addition, the internal resonance relationship also shows that the system can directly produce internal resonance phenomenon without the participation of oscillating mode, only through the interaction between respiration and deflection modes. Finally, when the stability of the system is studied, it is found that changing the magnitude of the magnetic field will cause the bifurcation phenomenon of the equilibrium point, as well as the hyperchaotic, quasi-periodic, and periodic motion states of the system under different parameter conditions.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
