7.4LINEARIZATION

Chapter 4 introduced a number of important concepts instrumental in analyzing the behavior of linear systems. By linear systems, we are referring to actual systems modeled by linear algebraic and differential equations. Real-world systems are inherently nonlinear. However, in certain regions, they may respond in a way that a linear model provides an acceptable representation of the system’s dynamics. Whenever we employ linear models to describe nonlinear systems, it must be with the understanding that the system remains within its so-called linear-operating region.

Consider the simple mechanical spring shown in Figure 7.47. Its deflection x from equilibrium depends on the magnitude and direction of the applied force F.

Figure ...

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