### Introduction

In this Section we introduce the concept of a transfer function and then use this to obtain a Laplace transform model of a linear engineering system. (A linear engineering system is one modelled by a constant coefficient ordinary differential equation.)

We shall also see how to obtain the impulse response of a linear system and hence to construct the general response by use of the convolution theorem.

#### Prerequisites

- be able to use the convolution theorem
- be familiar with taking Laplace transforms and inverse Laplace transforms
- be familiar with the delta (impulse) function and its Laplace transform

#### Learning Outcomes

- find a transfer function of a linear system
- show how some linear systems may be combined together by combining appropriate transfer functions
- obtain the impulse response and the general response to a linear engineering system

#### Contents

1 Transfer functions and linear systems2 Modelling linear systems by transfer functions

3 Engineering Example 3

3.1 System response