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ERIC Number: EJ863628
Record Type: Journal
Publication Date: 2009
Pages: 16
Abstractor: As Provided
Reference Count: 21
ISBN: N/A
ISSN: ISSN-0020-739X
Non-Linear Spring Equations and Stability
Fay, Temple H.; Joubert, Stephan V.
International Journal of Mathematical Education in Science and Technology, v40 n8 p1069-1084 2009
We discuss the boundary in the Poincare phase plane for boundedness of solutions to spring model equations of the form [second derivative of]x + x + epsilonx[superscript 2] = Fcoswt and the [second derivative of]x + x + epsilonx[superscript 3] = Fcoswt and report the results of a systematic numerical investigation on the global stability of solutions to initial value problems as the initial conditions are allowed to vary. We demonstrate that the unforced spring models explain some of the unbounded behaviour observed with the forced models and thus give at least an idea of where to expect bounded behaviour to occur. We also discuss the behaviour when viscous damping is added to the unforced models. (Contains 17 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A