### Introduction

In this Section we look at a typical application of Fourier series. The problem we study is that of a differential equation with a periodic (but non-sinusoidal) forcing function. The differential equation chosen models a lightly damped vibrating system.

#### Prerequisites

- know how to obtain a Fourier series
- be competent to use complex numbers
- be familiar with the relation between the exponential function and the trigonometric functions

#### Learning Outcomes

- solve a linear differential equation with a periodic forcing function using Fourier series

#### Contents

1 Modelling vibration by differential equation2 Applying Fourier series to solve a differential equation