Abstract: In this paper, taking the prolate cycloid-three-wire as amodel of physical dynamics, we consider the damping's influence on computationof workpiece's moment of inertia by using the second kind Lagrange'sequation. It is difficult to calculate the value of amplitude of swingaccurately by the amplitude measuring method. So, an equal arc length- timeratio method is proposed to improve the precision for a workpiece of largesize. The damping ratio \zeta is obtained bycalculating the time ratio of hanging dish which swings beyond the equalarc length in the same location with different periods.