In a rotor bearing system operating with constant angular acceleration, after passing through the critical speed, typical beat characteristics are observed because the transverse vibration response contains both excited and natural motion, and shortly after passing resonance, vibrations with close frequencies appear. The present study explains a method for estimating damping of rotor bearing systems from transient beat vibration signals observed during run up stage. A mathematical derivation to prove that a part of run-up vibration of the rotor system consists of beat phenomenon when the system crosses critical speed. It is also observed from the mathematical model that the beat vibrations depend on the damping in the system. This beat response is considered for Hilbert analysis and the damping is estimated. Increase in angular acceleration of the rotor will increase the damping. This paper investigates how the damping varies with respect to different angular acceleration values of the rotor bearing system. Experimental validation of the beat phenomenon and damping estimation are done for the rotor system. The proposed method is validated by using half-power band width method applied to run-up response.