abstract: A periodically driven system has discrete time-translation symmetry with the period of the driving. Generally, dynamical variables oscillate with the driving period. Recently much interest have attracted systems where the time symmetry is broken, the “time crystal” effect. Coupled nonlinear oscillators, including cold atoms, nanomechanical systems, and modes in electromagnetic cavities, provide an ideal platform for studying this effect. We will discuss the symmetry breaking in such systems and show that it is mediated by rare events. The symmetry-breaking transitions are different depending on the coupling between the vibrational systems. We will also discuss the Schrodinger bridge in driven vibrational systems.