International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 2, Pages 381-385

On the existence of periodic and eventually periodic solutions of a fluid dynamic forced harmonic oscillator

Charlie H. Cooke

Department of Mathematical Sciences, Old Dominion University, Norfolk 23508, Virginia, USA

Received 18 November 1985

Copyright © 1986 Charlie H. Cooke. 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.


For certain flow regimes, the nonlinear differential equation Y¨=F(Y)G, Y0, 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.