Linear, Cubic and Quintic Coordinate-Dependent Forces and Kinematic Characteristics of a Spring-Mass System

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dc.contributor.authorSarafian, Haiduke
dc.date.accessioned2018-05-15T07:55:28Z
dc.date.available2018-05-15T07:55:28Z
dc.date.issued2013-09
dc.description.abstractBy combining a pair of linear springs we devise a nonlinear vibrator. For a one dimensional scenario the nonlinear force is composed of a polynomial of odd powers of position-dependent variable greater than or equal three. For a chosen initial condition without compromising the generality of the problem we analyze the problem considering only the leading cubic term. We solve the equation of motion analytically leading to The Jacobi Elliptic Function. To avoid the complexity of the latter, we propose a practical, intuitive-based and easy to use alternative semi-analytic method producing the same result. We demonstrate that our method is intuitive and practical vs. the plug-in Jacobi function. According to the proposed procedure, higher order terms such as quintic and beyond easily may be included in the analysis. We also extend the application of our method considering a system of a three-linear spring. Mathematica [1] is being used throughout the investigation and proven to be an indispensable computational toolen_US
dc.identifier.citationWorld Journal of Mechanics, 2013, 3, 265-269en_US
dc.identifier.uridx.doi.org/10.4236/wjm.2013.36027
dc.identifier.urihttp://hdl.handle.net/123456789/1378
dc.language.isoenen_US
dc.subjectLinearen_US
dc.subjectCubic and Quintic Nonlinear Oscillationsen_US
dc.subjectSemi-Analytic Solution to Equation of Motionen_US
dc.subjectMathematicaen_US
dc.titleLinear, Cubic and Quintic Coordinate-Dependent Forces and Kinematic Characteristics of a Spring-Mass Systemen_US
dc.typeArticleen_US
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