Wilberforce Lite: Energy Evolution of a Doubly-Resonant Elastic Pendulum

A Wilberforce pendulum is a well-known system in which a mass bobbing on a vertical spring alternately shares energy between longitudinal and torsional oscillations. The geometry of a typical spring naturally couples these different oscillation modes. But the coupling itself makes the analysis of motion firmly beyond the level of an Introductory Physics course. There is a more-accessible system that can be analyzed in the Introductory Physics course (both experimentally and computationally). I do a lab in which students determine a spring constant both statically and dynamically. When a specific mass bobs vertically on a typical spring, the system begins swinging like a pendulum, and energy is periodically exchanged between these two oscillation modes. Interestingly, the bobbing frequency is exactly twice that of the swinging frequency. In my talk, I will discuss how to computationally model this system and compare the model to real data. I will also describe the equipment setup, and display the system's energy evolution on a ternary energy diagram.