### 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