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.)