Pursuing the Ubiquitous Pendulum

摘要

In this paper, we offer three examples, inspired by Galileo's work, for connecting the physics of the pendulum with free fall and the inclined plane. The first example discusses the time it takes for a ball to slide down a frictionless inclined plane along a chord, drawn from the lowest point of a vertical circle to any point on the circle. The second example discusses a timing method that Galileo tested in measuring free fall directly, and the third example outlines an approach we have developed for accurately calculating the period of a pendulum for any angle, using only the kinematics of accelerated motion along an inclined plane, first studied by Galileo.