Measurement of a moment of inertia of a sample piece under nonlinear damping condition

In order to measure the moment of inertia of a sample piece under nonlinear damping condition, the influence of nonlinear damping on the movement of a torsion pendulum was analyzed. The nonlinear motion equation of the torsion pendulum was established. The moment of inertia of a sample piece was calculated with instantaneous undamped natural frequency and the instantaneous decay coefficient of the torsion pendulum computed using Hilbert transformation. In order to increase the effect of the nonlinear damping, the damping paddles were used to increase the area of the sample piece. The moment of inertia of the sample piece was measured with a system based on a torsion pendulum. The experimental results showed that the relative error of the moment of inertia of the sample piece is less than 1% under condition of nonlinear damping.