### 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