Static Electric-Spring and Nonlinear Oscillations
H. Sarafian
DOI: 10.4236/jemaa.2010.22011   PDF    HTML   XML   8,008 Downloads   12,768 Views   Citations


The author designed a family of nonlinear static electric-springs. The nonlinear oscillations of a massively charged particle under the influence of one such spring are studied. The equation of motion of the spring-mass system is highly nonlinear. Utilizing Mathematica [1] the equation of motion is solved numerically. The kinematics of the particle namely, its position, velocity and acceleration as a function of time, are displayed in three separate phase diagrams. Energy of the oscillator is analyzed. The nonlinear motion of the charged particle is set into an actual three-dimensional setting and animated for a comprehensive understanding.

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H. Sarafian, "Static Electric-Spring and Nonlinear Oscillations," Journal of Electromagnetic Analysis and Applications, Vol. 2 No. 2, 2010, pp. 75-81. doi: 10.4236/jemaa.2010.22011.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] S. Wolfram, “The Mathematica book,” 5th Ed., Cambridge University Publications, 2003.
[2] E.g. J. Marion, “Classical dynamics of particles and systems,” 4th Ed., Harcourt College Publishers, 1995.
[3] G. Duffing, “Erzwungene schwingungen bei veranderlicher eigen-frequenz,” F. Vieweg und Sohn, Braunschweig, 1918.
[4] S. Strogatz, “Nonlinear dynamics and chaos,” Perseus Publishing, 1994.
[5] http://wow.scalped.orgy/article/Duffing_oscillator.
[6] R. H. Ennis and G. C. McGuire, “Nonlinear physics with Mathematica for scientists and engineers,” Published by Birdhouse, Hard Spring, Peg 605, 2001.
[7] E.g. J. D. Jackson, “Classical electrodynamics,” 3rd Ed., Wiley, 2005.

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