A slender, uniform rod is free to rotate on a horizontal frictionless table about a pivot at a distance x from its midpoint, with one of the ends supported by a spring. Once the rod is displaced by a small angle from the equilibrium position and released, it will move in angular simple harmonic motion (SHM), and in textbooks, students are asked to determine the period of this motion, but usually only when the rod is pivoted at its center (i.e., when x = 0). In this short note, it is shown that the period is a simple, smooth function of x, whose analysis reveals that it is exactly the same when the rod is pivoted at the endpoint or the midpoint.
In introductory physics courses, undergraduate students have their first contact with the dynamics of rotating bodies, then learn how to adapt Newton’s second law of motion...
