Effects of the rigid rotation on the eigen-frequency, modal and dynamical response of a double degree-of-freedom mass-springs vibration system are clarified in the paper and the results provide important guidance for the rigid-flexible coupling dynamics of general elastic bodies and structures. There are two dynamic frequencies for the centrifugal vibration system in which the first order dynamic frequency decreases but second order dynamic frequency increase linearly with grow up of rigid rotation. Dynamical response of the mass is expressed by the mass trajectory evolution which is associated with the vibrating initial conditions, rigid rotational speed, initial eccentric position and vibration stiffness. The mass trajectory is composed of the non-eccentric vibrating portion and the eccentric vibrating portion, in which the former portion is dependent of vibration initial conditions, rigid rotation speed and vibration stiffness and the latter portion is determined by the initial centrifugal position, rigid rotational speed and vibration stiffness but nothing to do with the vibration initial conditions. In the light of the dynamic frequency and dynamical response of the system, the maximum and critical rigid rotational speeds are proposed in the paper for the centrifugal vibration system with two degrees of freedom.