Linearity
A linear system is any system which, when any input is applied, provides one, unique solution. Any system which provides more than one solution for a given input is non-linear.
An example of a linear system would be $ y(t) = 20x(t-5) $.
When provided with the input $ x(t) = t^2 $, the equation becomes:
$ y(t) = 20(t-5)^2 = 20(t^2 - 10t + 25) = 20t^2 - 200t + 500 $.
When a second input: $ x(t) = 1/5t $ is provided, the equation becomes:
$ y(t) = 4(t-5) = 4t - 20 $
If these two inputs were added together and put through the system, the answer should be the same as if the individual outputs were added up. This will show linearity.
$ x(t) = t^2 + 1/5t $ Here is the total input.
$ y(t) = 20(t-5)^2 + 4(t-5) $
As can be seen, the final function y(t) is equal to the sum of the individual parts.
A nonlinear system would be any system which does not fulfill that property. A good example of this is $ y(t) = x(t)^2 $.
