Peak-Frequency Responses and Tuned Mass Dampers-Exciting Applications of Systems of Differential Equations

Abstract

We present two applications of systems of ordinary differential equations concerning excitation of a structure through resonance and we investigate peak-frequency responses and stabilization by means of a tuned mass damper (TMD). The physics, engineering, and mathematics associated with these phenomena are presented and discussed along with illustrations of how to use this material with students.

Introduction

The study of differential equations, while often taught in a mathematics department as a course in solution techniques sprinkled with applications, could serve as a tool for modeling physical phenomena, thus motivating students to want to learn more about solution strategies and their interpretation.