Damping mechanisms of a pendulum

Abstract

In this paper, we study the damping mechanisms of a pendulum. The originality of our setup is the use of a metal strip suspension and the development of extremely sensitive electric measurements of the pendulum velocity and position. Their sensitivity is absolutely necessary for a reliable measurement of the pendulum damping time constant because this measurement is possible only for very low oscillation amplitudes, when air friction forces quadratic in velocity have a negligible contribution to the observed damping. We have thus carefully studied damping by air friction forces, which is the dominant mechanism for large values of the Reynolds number Re but which is negligible in the Stokes regime, . In this last case, we have found that the dominant damping is due to internal friction in the metal strip, a universal effect called anelasticity, and, for certain frequencies, to resonant coupling to the support of the pendulum. All our measurements are well explained by theory. We believe this paper would be of interest to students in an undergraduate classical mechanics course.