In this paper, a symmetric gyro with coupling to the tip mass of a beam mounted on a vibrating base is considered. Taking advantage of the angular momentum of the rotating gyroscope, gyrostabilizer systems are expected to become more widely actualized as they provide an effective means of motion control with several significant advantages for various structures. This paper mainly focused on finding optimized stiffness and damping values that minimize the vibration responses with the derivation of the frequency equations of a special combined gyro-beam system. Correctness of the analytical results is verified by numerical simulations. The comparison with the results from the derivation of the corresponding frequency equations shows that the optimized stiffness and damping values are very accurate.