A physical model of the sinc function: The center-of-mass spiral

Abstract

The sinc function, defined as sinc(x)=sin(x)/x, is a fundamental tool in applied mathematics and physics, arising in fields ranging from signal processing to quantum mechanics. This paper presents a novel physical interpretation of the sinc function in the context of classical mechanics: it describes the trajectory of the center of mass of a thin thread winding around a circular core. As the thread winds around the core, its center of mass oscillates in a pattern described by the sinc function. When viewed in two dimensions, the full trajectory forms a distinctive spiral, which we term the “center-of-mass spiral.” This concept can generalize to arbitrary winding core shapes and thread densities. This physical model provides an intuitive and pedagogically valuable demonstration for physics instruction, connecting abstract mathematical functions to tangible mechanical processes.