In this lecture we first understand the behaviour of the dynamical system qualitatively using a simple analogy and then use a numerical technique to simulate the behaviour of the system in an example.

The differential equations of a single machine infinite bus(SMIB) system are similar to that of a "mass connected to a wall by a nonlinear spring" system.

For a linear spring, the restoring force is directly proportional to the stretch of the spring. If the mass is displaced from its equilibrium, then oscillatory motion results irrespective of the extent of the disturbance.

If the restoring force of the spring is a nonlinear function of the stretch, then the behavior may be different and depends on the extent of the disturbance.