Large oscillations of the trifilar pendulum: Analytical and experimental study

The trifilar pendulum is one of the most widely used methods for the measurement of the moment of inertia of a body around a rotating axis. Despite its simplicity, this method allows very high accuracy. In general, the motion of the pendulum is assumed to be small enough to be considered linear. However, some applications exist for which larger motions have to be employed. In these cases, the amplitude of the motion influences the period of oscillation of the pendulum and affects the moment of inertia measured value. To avoid such errors, the nonlinear motion of the pendulum in large oscillation conditions has to be considered. In this paper, the large motion of the pendulum is investigated analytically, numerically and experimentally. From these analyses, the situations where the nonlinearities of the motion of the pendulum have more influence on the accuracy are identified and described. The most important parameters influencing the period of oscillation are highlighted. The analyses show that by a proper and simple instrumentation of the pendulum, highly accurate results can be obtained also for large motion amplitudes. A calibration technique able to consider the most important nonlinearities in the motion of the pendulum is presented.