The Ping Pong Pendulum

TL;DR

This paper investigates a simple mechanical pendulum that demonstrates increasing oscillation frequency as its amplitude diminishes, similar to phenomena observed in systems like Euler's Disk, highlighting unique damping behaviors.

Contribution

It introduces a basic pendulum model that exhibits increasing frequency during damping, providing insights into non-standard oscillatory damping behaviors.

Findings

Pendulum's frequency increases as amplitude decreases.

Demonstrates damping behavior similar to Euler's Disk.

Provides a simplified model for studying such phenomena.

Abstract

Many damped mechanical systems oscillate with increasing frequency as the amplitude decreases. One popular example is Euler's Disk, where the point of contact rotates with increasing rapidity as the energy is dissipated. We study a simple mechanical pendulum that exhibits this behaviour.