In this note we describe some aspects of synchronization problem of a system of pendulums connected with rigid body free in horizontal motion. Results of numerical simulation for the system of four non-identical pendidum.s are presented. Possible synchronization modes of the system for some sets of data are shown. Amplitudes of motion of the mass centre of the whole system, as well as relative motion of pendulums' mass centres are analysed. Evolution of the system motion from transient to unstable synchronization through desynchronization to stable synchronization is shown. Finally the attempt to explain the mechanism of pendulums synchronization was taken.