The clearances, which universally exist in the joint parts of mechanical systems, are a main cause of various operation deteriorating problems, including noises generating, material wearing, even the early fatigue of members. In this paper, a new method to determine the clearance magnitude in the beam support is proposed with the description of a numerical example. The growing clearance will increase the vibration period of realistic system, and the accurateness of measurement is relevant to the frequency resolution of the instrument. Through the time series of the midpoint response of a simply supported beam, the period of the first modal free vibration can be obtained using the FFT Algorithm. Only two responses from different initial conditions are needed to identify the magnitude of the clearance. It is estimated the accurateness could be below 15%. The investigation also suggests this free vibration period approach may be adapted to handle the energy losses situations with the damping ratio considered in the formulas.