This study presents a new balancing method that utilizes the equations of motion associated with the rotor dynamics system. While the conventional balancing method includes calculation of mass unbalance based on so-called as-is and trial-run techniques, the proposed approach computes mass unbalance by only applying the as-is technique and further explains the critical speed and the damping ratio. A simple test rig was employed to validate the efficacy of the proposed method. A non-central rotor system was utilized as the experimental model, the actual value of the rotor system’s mass eccentricity was measured according to ISO 1940/1-1986(E), and with a comparison done using the results obtained by applying the proposed method. The sensitivity of the measurement error was compared with that of the conventional approach which utilizes the influence coefficient method.