Radial Forcing and Edgar Allan Poe's Lengthening Pendulum

TL;DR

This paper explores how radial forcing can parametrically amplify a pendulum's oscillations, inspired by Poe's story, through numerical modeling and analysis of complex harmonic motion.

Contribution

It introduces a numerical model demonstrating how timed radial forcing can increase pendulum oscillations, providing educational insights into parametric amplification.

Findings

Radial forcing can parametrically amplify pendulum oscillations.

Uniform lengthening does not increase oscillation amplitude.

Properly timed radial forcing enhances oscillation amplitude.

Abstract

Inspired by Edgar Allan Poe's The Pit and the Pendulum, we investigate a radially driven, lengthening pendulum. We first show that increasing the length of an undriven pendulum at a uniform rate does not amplify the oscillations in a manner consistent with the behavior of the scythe in Poe's story. We discuss parametric amplification and the transfer of energy (through the parameter of the pendulum's length) to the oscillating part of the system. In this manner radial driving may easily and intuitively be understood, and the fundamental concept applied in many other areas. We propose and show by a numerical model that appropriately timed radial forcing can increase the oscillation amplitude in a manner consistent with Poe's story. Our analysis contributes a computational exploration of the complex harmonic motion that can result from radially driving a pendulum, and sheds light on a mechanism by which oscillations can be amplified parametrically. These insights should prove especially valuable in the undergraduate physics classroom, where investigations into pendulums and oscillations are commonplace.