Nonlinear Oscillations of a Magneto Static Spring-Mass ()
Abstract
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
References
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G. Duffing, “Erzwungene Schwingungen bei Veranderlicher Eigen-frequenz,” F. Vieweg und Sohn, Braunschweig, 1918.
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S. Wolfram, “The Mathematica Book,” 5th Edition, Cambridge University Publications, Cambridge, 2003, and MathematicaTM software V8.0, 2011.
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