Basically, why is it important we know about nonlinearity? Please, if possible write in a bit more detail than a line if you can, otherwise any answer is still appreciated.
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Linearity of a system is a property that makes everything easy. There are countless analytical tools available that can be applied to linear systems, so if a system is highly linear, engineers piss themselves with glee and go to work at it.
Unfortunately, no real system is truly completely linear, and some systems are extremely nonlinear. For example, the force of air resistance on a moving body is proportional to the square of its velocity--a nonlinear effect. To deal with nonlinear systems, engineers use linearization techniques (expand functions in a Taylor series around an equilibrium point) to treat the system as linear in a certain neighborhood. Continuing with the example, if a plane is flying at an average speed of, say, 200 meters per second, you can linearize the expression for air resistance around this speed. That way, changes in the speed around that 200 m/s--say from 190 m/s to 210 m/s--produce linear changes in the air resistance.
The reason it's important to know about nonlinearities is that the assumptions you make--like that the airplane is flying at about 200 m/s--are not always valid. The plane will slow down, speed up, land, take off, crash, etc. Treating a system as linear is convenient and useful, but not at all complete.
Unfortunately, no real system is truly completely linear, and some systems are extremely nonlinear. For example, the force of air resistance on a moving body is proportional to the square of its velocity--a nonlinear effect. To deal with nonlinear systems, engineers use linearization techniques (expand functions in a Taylor series around an equilibrium point) to treat the system as linear in a certain neighborhood. Continuing with the example, if a plane is flying at an average speed of, say, 200 meters per second, you can linearize the expression for air resistance around this speed. That way, changes in the speed around that 200 m/s--say from 190 m/s to 210 m/s--produce linear changes in the air resistance.
The reason it's important to know about nonlinearities is that the assumptions you make--like that the airplane is flying at about 200 m/s--are not always valid. The plane will slow down, speed up, land, take off, crash, etc. Treating a system as linear is convenient and useful, but not at all complete.
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Non-linearity produces distortion and error. In an analog system, non-linearity would produce distortion in the signal. For instance, in analog video, non-linearity will cause brightness artifacts. In a digital system, non-linearity can cause errors in the transmitted data.