Abstract
The paper discusses the boundary in the frequency–amplitude plane for boundedness of solutions to the forced spring Duffing type equation For fixed initial conditions and for representative fixed values of the parameter ϵ, the results are reported of a systematic numerical investigation into the global stability of solutions to the initial value problem as the parameters F and ω 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 indicate that the low resonance frequency (to two decimal places) is independent of the value of ϵ and that near a higher jump frequency phenomena the behaviour of solutions is very unstable. Computer laboratory problems suitable for student research and small group projects are included.
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