Huygens' clocks: 'sympathy' and resonance

The paper presents a numerical and experimental study of a setup which mimics the famous 'sympathy' of pendulum clocks experiment conducted by Christian Huygens. The setup consists of two pendula (metronomes) installed on a platform which can move either in horizontal or vertical direction. Existence and co-existence of different synchronisation regimes is studied both experimentally and numerically. The main contribution of the paper reveals that the stability onsets of those modes resemble behaviour of systems with auto-parametric resonance. Therefore, the resonances of translational frequency of the platform and rotational frequency of metronomes induce different types of synchronous behaviour. This novel approach turns out to be more insightful then an analysis of how the platform mass and/or the spring stiffness influence the stability onsets.