ERIC Number: EJ753899
Record Type: Journal
Publication Date: 2006-Jul-15
Pages: 7
Abstractor: Author
ISBN: N/A
ISSN: ISSN-0020-739X
EISSN: N/A
Nonlinear Resonance and Duffing's Spring Equation
Fay, Temple H.
International Journal of Mathematical Education in Science & Technology, v37 n5 p593-599 Jul 2006
This note discusses the boundary in the frequency--amplitude plane for boundedness of solutions to the forced spring Duffing type equation. For fixed initial conditions and fixed parameter [epsilon] results are reported of a systematic numerical investigation on the global stability of solutions to the initial value problem as the parameters F and [omega] are allowed to vary. This can be interpreted as varying the forcing amplitude and forcing frequency to a nonlinear spring problem and asking for the threshold between bounded oscillatory responses and unbounded unstable responses. These preliminary results show interesting behaviour, illustrate a low resonance frequency and a higher jump frequency phenomena, and give rise to computer laboratory problems suitable for student research and small group projects. (Contains 3 figures.)
Descriptors: Student Research, Computer Uses in Education, Equations (Mathematics), Mathematics Instruction, Problem Solving, Calculus, Science and Society, Computer Software, Teaching Methods
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: N/A
Audience: N/A
Language: English
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