Abstract:  Synchronization is one of the most popular phenomena in nature, which is critical to our understanding on the behaviors of many complex systems. In this paper, we investigate numerically the influence factors, including the mass ratio between the beam and the pendulum, the mass difference as well as the length difference of the two coupled pendulums, to the occurrence of measure synchronization between two pendulums suspended from a common beam utilizing the MATLAB software. When the two coupled pendulums are identical, as the mass ratio R between the beam and the pendulum decreases, the interacting strength between the two pendulums will be increased. As R is decreased to be smaller than a threshold value, the two pendulums can achieve measure synchronization and their phase difference is kept fixed as π. When the mass difference or the length difference of the two pendulums is increased, the interacting strength of the two pendulums will be decreased and the pendulums will be desynchronized. 

Key words: coupled pendulums, measure synchronization, anti-phase synchronization, Matlab simulation