Synchronization Analysis of Christiaan Huygens' Coupled Pendulums

This paper discovers a new finding regarding Christiaan Huygens' coupled pendulums. The reason Christiaan Huygens' coupled pendulums obtain synchrony is that the coupled pendulums are subject to a harmonic forcing. As the coupled pendulums swing back and forth, they generate a harmonic force, which, in turn drives the coupled pendulums, such that the two pendulums swing in synchrony once the angular frequency of the generated harmonic forcing satisfies a certain condition. The factor that determines the angular frequency of the generated harmonic forcing is the effective length of the pendulum, as its angular frequency solely depends on the length of the pendulum that swings about a fixed point. In other words, it is the effective length of the coupled pendulum that determines whether the coupled pendulum achieves synchrony or not. The novelty of this article is that the author explains and analyzes the synchronization behaviour of Christiaan Huygens' coupled pendulums from the frequency and harmonic-forcing perspectives.