When Two Coupled Pendulums Equal One: A Synchronization Machine

We show that two coupled pendulums that are coupled and can synchronize, are mathematically equivalent to one "horizontal" parametrically driven pendulum. We have fabricated a horizontal pendulum and present data from this horizontal pendulum which we believe to be the first physical realization of such a mechanical "synchronization machine." A description of intermittent synchronization that can occur when two coupled pendulums are in a chaotic state is given in terms of the data from the horizontal pendulum. We discuss the relationship between the modes of the horizontal pendulum and the corresponding synchronization of the two coupled pendulums. Finally, we show that when a horizontal pendulum is driven by any random source, not necessarily chaotic, intermittent synchronization can occur.