Document Type
Article
Publication Date
1986
DOI
10.1155/s0161171286000479
Publication Title
International Journal of Mathematics and Mathematical Sciences
Volume
9
Issue
2
Pages
381-385
Abstract
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 the fan.
Original Publication Citation
Cooke, C. H. (1986). On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator. International Journal of Mathematics and Mathematical Sciences, 9(2), 381-385. doi:10.1155/s0161171286000479
Repository Citation
Cooke, Charlie H., "On the Existence of Periodic and Eventually Periodic Solutions of a Fluid Dynamic Forced Harmonic Oscillator" (1986). Mathematics & Statistics Faculty Publications. 77.
https://digitalcommons.odu.edu/mathstat_fac_pubs/77
Comments
This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright © 1986 Hindawi Publishing Corporation.