Kissing the cheeks of Huygens

Abstract

How well do the so-called cheeks of Huygens enforce a constant time of oscillation on a pendulum, independent of the amplitude of the pendulum swing? We use a video measurement tool to test it with a homemade experimental setup that can be fruitfully used in classroom and physics laboratory settings. Data fits reveal how well the setup confirms the usefulness of the cheeks of Huygens. Comparisons of computer model results with recorded data have been made for the same purpose. The equation of motion of a pendulum with a string of arbitrary length that winds along two surfaces of cycloidal cheeks is derived, too. Numerical solutions of this equation are used for the error analysis of measurements with the homemade setup.