From the compound pendulum to a falling weighted rod: a case for dynamical modeling?

Abstract In this work we highlight the synthesizing power of the dynamical modeling by comparing quantitatively two experiments, usually not related to each other. This is possible because on the one hand the same physical device, a rigid rod with an additional load that can be moved to different positions along it, can be used either as a physical pendulum performing small-amplitude oscillations or behaving as a falling rod. On the other hand, because modern numerical softwares for dynamical modeling do not require linearization with respect to the angle of the restoring force, thus providing the time evolution of the angular position even in the case of large amplitudes. The quantitative analysis of the experimental data yields an interesting property: for any two arbitrarily chosen load positions, the falling times of the rod are always related by the same proportionality factor, regardless of the choice of the initial and final angles.