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== Examples of Linear and Non-Linear Systems == | == Examples of Linear and Non-Linear Systems == | ||
| + | |||
| + | y(t)= 3x(t) | ||
| + | <pre> | ||
| + | x(t)-->|System|-->|*a| | ||
| + | > ax(t)+bx(t) | ||
| + | x(t)-->|System|-->|*b| | ||
| + | </pre> | ||
| + | <pre> | ||
| + | x(t)-->|*a| | ||
| + | > |System|--> ax(t)+bx(t) | ||
| + | x(t)-->|*b| | ||
| + | </pre> | ||
| + | y(t)= 3x(t) Results with the same answer given the both equations and is therefore linear. | ||
| + | |||
| + | |||
| + | y(t)= 3*sqrt(x(t)) | ||
| + | <pre> | ||
| + | x(t)-->|System|-->|*a| | ||
| + | > a*sqrt(x(t))+b*sqrt(x(t)) | ||
| + | x(t)-->|System|-->|*b| | ||
| + | </pre> | ||
| + | <pre> | ||
| + | x(t)-->|*a| | ||
| + | > |System|--> sqrt(ax(t)+bx(t)) | ||
| + | x(t)-->|*b| | ||
| + | </pre> | ||
| + | y(t)= 3*sqrt(x(t)) yeilds different results in both cases and is therefore Non-linear. | ||
Latest revision as of 09:00, 11 September 2008
Linear System
A linear system is a system in which you can send the sum of any inputs and when you compare the outputs to the inputs, the outputs contain the same coefficients as the corresponding inputs.
Examples of Linear and Non-Linear Systems
y(t)= 3x(t)
x(t)-->|System|-->|*a|
> ax(t)+bx(t)
x(t)-->|System|-->|*b|
x(t)-->|*a|
> |System|--> ax(t)+bx(t)
x(t)-->|*b|
y(t)= 3x(t) Results with the same answer given the both equations and is therefore linear.
y(t)= 3*sqrt(x(t))
x(t)-->|System|-->|*a|
> a*sqrt(x(t))+b*sqrt(x(t))
x(t)-->|System|-->|*b|
x(t)-->|*a|
> |System|--> sqrt(ax(t)+bx(t))
x(t)-->|*b|
y(t)= 3*sqrt(x(t)) yeilds different results in both cases and is therefore Non-linear.
