Previous research has reported changes in mu rhythm, the central rhythm of the alpha frequency band, in both intentional and spontaneous interpersonal coordination. The current study was designed to extend existing findings on social synchrony to the pendulum swinging task and simultaneously measured time unfolding behavioral synchrony and EEG estimation of mu activity during spontaneous, intentional in-phase and intentional anti-phase interpersonal coordination. As expected, the behavioral measures of synchrony demonstrated the expected pattern of weak synchronization for spontaneous coordination, moderate synchronization for intentional anti-phase coordination, and strong synchronization for in-phase coordination. With respect to the EEG measures, we found evidence for mu enhancement for spontaneous coordination in contrast to mu suppression for intentional coordination (both in phase and anti-phase), with higher levels of synchronization associated with higher levels of mu suppression in the right hemisphere. The implications of the research findings and methodology for understanding the underlying mechanisms contributing to social problems in psychological disorders, leader-follower relationships, and inter-brain dynamics are discussed.