Module 1 : Introduction and Background Material
Lecture 1 : Introduction
 
1 Linear versus nonlinear response
A common method of exploring properties of a physical system is to study its response to a probe or stimulus. There exists a functional relationship between the effect E and stimulus S. Dependence of E on S is the system's property. Depending upon whether this relationship linear or nonlinear, a system called linear or nonlinear.
1.1 Some Illustrations:

We start with a familiar example of a mechanical system - a simple pendulum shown in figure 1, which, when displaced (stimulus) from equilibrium, executes oscillatory motion with variable acceleration (effect) - under the gravitational force component directed towards the equilibrium position. The equation of motion is
 
(1.1)
Figure1.1: motion of a simple pendulum