Motor Banter: Experiments on Dynamic Synchronization

John Kolinski, Physics, UIUC

We study a set of eccentrically weighted DC motors (cell phone vibrators) attached to a flexible plate and find that they synchronize, and do so in accord with predictions based solutions of a Kuramoto-like equation for coupled phase oscillators. These equations differ from the familiar in that coupling, both phase and magnitude, is an irregular function of frequency and motor position. A mathematical model for the mechanical system is developed and key parameters are identified, including the plate's natural modes of vibration and their Q's, (or more generally the Greens' function of the plate) the number of motors, their eccentric mass and their internal viscous drag. Predictions are extracted for the threshold of synchronization as a function of the number of motors and the plate's Q, and confirmed in the laboratory. Frequency-time plots showing the synchronization dynamics and acoustic energy output elucidate some of the complex dynamics of our system. A video of synchronization will be shown.