We experimentally demonstrate vibration phase reversal transition in a discrete time-translational symmetry broken cold atomic system by the application of a pulsed bias-field opposite to the existing phase of the symmetry broken vibrational state. The reversal transition depends on the strength h(p) and the duration Delta t of the applied pulse. Consequently, we obtain a h(p) - Delta t phase boundary with a divergent relaxation time tau due to the critical slowdown behavior. Interestingly, the dependence of the dynamic phase boundary and relaxation time on the noise-induced switching rate implies that the system is out of equilibrium, though not so in the Ising model of a spin system. (C) 2019 Optical Society of America