Elastic actuators find a growing interest in many research areas ranging from rehabilitation robotics to industrial robotics. Elastic actuators are actuators with elements of compliance, such as springs connected in different configurations between the actuator and the load. In particular, Rigid Parallel Series Elastic Actuators (RPSEA) is an emerging design that, in addition to the advantages provided by parallel elastic actuators, provides the ability to actively control the storage and release of spring energy. Owing to the spring element in these actuators, they often face the problem of oscillations. In this study, we propose an energy-based control strategy for vibration suppression by using only one motor of the RPSEA. The analytical findings are substantiated with simulations of the mechanism subjected to an impulse disturbance.