Clustering and synchronization of n Huygens’ clocks

We study the synchronization of a number of pendulum clocks hanging from an elastically fixed horizontal beam. It has been shown that after a transient, different types of synchronization between pendulums can be observed: (i) the complete synchronization in which all pendulums behave identically, (ii) pendula create three or five clusters of synchronized pendulums, (iii) antiphase synchronization in pairs (for even n). We give evidence why the configurations with a different number of clusters are not observed. We argue that these phenomena are robust and can be observed experimentally.