Synchronization of Pendulums (Numerical Study)

Abstract

This paper presents the results of a numerical study of synchronization of pendulums, chronometers, and mechanical clocks suspended from a common movable beam. An auxiliary problem is considered about the oscillations of a pendulum with a swinging weight, then the mutual synchronization of free vibrations of two and four pendulums (and pendulums with the supply of a moment pulse-clock) on a common movable spring-loaded beam. It is shown that in the considered simplest configuration, mutual synchronization (equality of frequencies or oscillation periods) is performed with high efficiency. The frequency of synchronized oscillations of the pendulums is close to the frequency of vibrations of the platform in a wide range of changes in its rigidity. The degree of connectivity of pendulums and synchronization of their oscillations is determined by the Strouhal number. Synchronization of clocks does not guarantee the accuracy of their movement, which is achieved only when the Strouhal number is equal to one.