Damping effects induced by a mass moving along a pendulum

The experimental study of damping in a time-varying inertia pendulum is presented. The system consists of a disk travelling along an oscillating pendulum: large swinging angles are reached, so that its equation of motion is not only time-varying but also nonlinear. Signals are acquired from a rotary sensor, but some remarks are also proposed as regards signals measured by piezoelectric or capacitive accelerometers. Time-varying inertia due to the relative motion of the mass is associated with the Coriolis-type effects appearing in the system, which can reduce and also amplify the oscillations. The analytical model of the pendulum is introduced and an equivalent damping ratio is estimated by applying energy considerations. An accurate model is obtained by updating the viscous damping coefficient in accordance with the experimental data. The system is analysed through the application of a subspace-based technique devoted to the identification of linear time-varying systems: the so-called short-time stochastic subspace identification (ST-SSI). This is a very simple method recently adopted for estimating the instantaneous frequencies of a system. In this paper, the ST-SSI method is demonstrated to be capable of accurately estimating damping ratios, even in the challenging cases when damping may turn to negative due to the Coriolis-type effects, thus causing amplifications of the system response.