Most interesting and practical systems have nonlinear dynamics. Consider the spring and damper system presented in Figure 2.83. The spring is nonlinear such that the spring force and displacement are related as follows:

\[f_{s}(t)=2 x_{s}{ }^{2}(t)\]

The applied force is given by

\[f(t)=14+\delta f(t)\]

Find the linearised State-Variable Matrix model of the nonlinear system.

Nonlinear spring 0000 1 kg x(t) f(t) H H H H H H H Figure 2.83 Nonlinear dynamic system.