Influence of rotation speed on natural frequency: A short introduction and presentation of an imaginary 'antigravity' world

TL;DR

This paper introduces a teaching approach for resonance in rotating spring-mass systems, highlighting how rotation speed affects natural frequency and contrasting it with an imaginary 'antigravity' world where this dependency is absent.

Contribution

It extends traditional resonance teaching from translational to rotating systems, emphasizing the role of centripetal force and providing analytical solutions.

Findings

Natural frequency depends on rotation speed as a vector sum.

Resultant ground force remains harmonic despite rotation.

Imaginary 'antigravity' world shows no dependency of natural frequency on rotation.

Abstract

We present an instructive way to introduce the subject of resonance using a typical spring-mass system without damping. In contrast to the standard approach found in most textbooks, here we propose a way to extend the lectures from common translational systems to rotating ones. In the latter case, particular attention is paid to the role of the variable centripetal force. The students will find analytical solutions of the simplest possible ordinary differential equations of motion and see that the natural frequency strongly depends on the rotation speed, the latter being a simple vector sum. The analysis reveals that always the resultant ground force is harmonic. In order to depict the significance in the influence of rotation on natural frequency, we present an imaginary 'antigravity' world in which the aforementioned dependency is absent.