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Nonlinear Oscillations of a Magneto Static Spring-Mass

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Author(s): Haiduke Sarafian

Journal: Journal of Electromagnetic Analysis and Applications
ISSN 1942-0730

Volume: 03;
Issue: 05;
Start page: 133;
Date: 2011;
Original page

Keywords: Extended Duffing Equation | Magneto Static Spring | Damped Nonlinear Oscillations | Mathematica

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.
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