Definition of Linearity

A system is said to be linear if it meets the following two criteria:

1. If input x to the system results in output X, then an input of 2x will produce output of 2X. In other words, the magnitude of the system output is proportional to the magnitude of the system input.

2. If input x produces output X, and input y produces output Y, then an input of x + y will produce an output of X + Y. In other words, the system handles two simultaneous inputs independently, and they do not interact within the system. Implicit in these criteria is the fact that a linear system will not produce any frequencies in the output that are not present in the input.

Note that there is nothing in these criteria that says the system output is the same as the system input, or even that it resembles the system input. For instance, the input could be an electric current, and the output could be a temperature. In the case of mechanical structures such as machines, we will consider the input to be a vibratory force and the output to be the measured vibration itself.

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