Synchronization of pendulum clocks and metronomes: a qualitative treatment

Abstract Pendulum clocks and metronomes have in common the fact that they are self-excited oscillators, exhibiting stationary oscillations where an external energy input compensates losses due to damping. In the phase plane these oscillations are represented by closed trajectories called limit cycles, and the motion along them can be parameterized by a phase angle. In this work we investigate the dynamics resulting from the coupling between two phase oscillators, using average equations for the resonant cases. The results from this analysis are used to qualitatively describe phase locking and synchronization phenomena in phase oscillators, explaining results observed in the coupling of pendulum clocks and metronomes.