The vibration of a rotor rubbing a staler caused by an initial perturbation was studied analytically. The analytical model consists of a simple disc shaft rotor and a fixed slator. The perturbation is an instantaneous change of the radial velocity when the rotor is operating in its normal steady state. The analysis showed that the rotor may continue rubbing the stator for small clearance, even if the initial perturbation no longer exists. For the interest of engineering applications, we investigated various rotating speeds, perturbalion amplitudes and clearances between the rotor and the stator, Various friction coefficients on the contact surface were also considered. The graphical results can be used for the design of rotating machines.