On the synchronization of two metronomes and their related dynamics

Synchronization was first reported by Christiaan Huygens in 1665 when he observed anti-phase synchronization achieved by two pendulum clocks hanging on a common base. Since then researchers have tried to understand the results reported by Huygens using their own ways to reproduce his experiment and applying several methods of analysis. Each researcher has reported different results, even compared with those reported by Huygens. In this paper a simple model is proposed to study in-phase and anti-phase synchronization of two metronomes based on a normal mode analysis using van der Pol oscillators. The instantaneous frequency of the responses from both simulations and experimental data is used in the analysis. Unlike previous studies, measurements are made using videos and the time domain responses of the metronomes extracted by means of tracking software. Plots showing how the initial conditions lead to both synchronization states are also presented.