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The Duffing equation describes the oscillations of a damped nonlinear oscillator 1. Its non-linearity is confined to a one coordinate-dependent cubic term. Its applications describing a mechanical system is limited e.g. oscillations of a theoretical weightless-spring. We propose generalizing the mathematical features of the Duffing equation by including in addition to the cubic term unlimited number of odd powers of coordinate-dependent terms. The proposed generalization describes a true mass-less magneto static-spring capable of performing highly non-linear oscillations. The equation describing the motion is a super non-linear ODE. Utilizing Mathematica 2 we solve the equation numerically displaying its time series. We investigate the impact of the proposed generalization on a handful of kinematic quantities. For a comprehensive understanding utilizing Mathematica animation we bring to life the non-linear oscillations.

KEYWORDS

Extended Duffing Equation, Magneto Static Spring, Damped Nonlinear Oscillations, Mathematica

Cite this paper

H. Sarafian -Nonlinear Oscillations of a Magneto Static Spring-Mass,- Journal of Electromagnetic Analysis and Applications, Vol. 3 No. 5, 2011, pp. 133-139. doi: 10.4236-jemaa.2011.35022.





Author: Haiduke Sarafian

Source: http://www.scirp.org/



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