TITLE:
Nonlinear Oscillations of a Pair of Charged Rings
AUTHORS:
Haiduke Sarafian
KEYWORDS:
Nonlinear Oscillations, Charged Ring-Ring Electrostatic Interaction, Computer Algebra System, Mathematica
JOURNAL NAME:
American Journal of Computational Mathematics,
Vol.10 No.4,
December
10,
2020
ABSTRACT: Two electrically charged rings of different sizes are assembled along their common vertical symmetry axis through their centers. The bottom ring is secured on a horizontal support while the top one is loose. For a set of practical values characterizing the charged rings we envision a scenario where the mutual electric repulsion between the rings and the weight of the top ring results in stable nonlinear oscillations. To quantify the characteristics of the oscillations, we utilize a Computer Algebra System specifically Mathematica [1]. We accompany the analysis with a simulation for a comprehensive visual understanding.