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Full-Text Articles in Non-linear Dynamics
On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke
On The Existence Of Periodic And Eventually Periodic Solutions Of A Fluid Dynamic Forced Harmonic Oscillator, Charlie H. Cooke
Mathematics & Statistics Faculty Publications
For certain flow regimes, the nonlinear differential equation Y¨=F(Y)−G, Y≥0, G>0 and constant, models qualitatively the behaviour of a forced, fluid dynamic, harmonic oscillator which has been a popular department store attraction. The device consists of a ball oscillating suspended in the vertical jet from a household fan. From the postulated form of the model, we determine sets of attraction and exploit symmetry properties of the system to show that all solutions are either initially periodic, with the ball never striking the fan, or else eventually approach a periodic limit cycle, after a sufficient number of bounces away from …