| Line 7: | Line 7: | ||
Example for a linear system is | Example for a linear system is | ||
| − | <math>x_1</math> = 8<math>e^t</math> | + | <math>x_1</math> = 8<math>e^t</math> |
| + | |||
| + | <math>x_2</math>=8<math>t^2</math> | ||
| + | |||
| + | Let , | ||
| + | |||
| + | <math>x_3</math> = 8<math>e^t</math> + 8<math>t^2</math> | ||
Revision as of 14:21, 12 September 2008
A system is said to be linear if it follows the following conditions
1) The response to $ x_1(t) $ + $ x_2(t) $ is $ y_1(t) $ +$ y_2(t) $.
2) The response to $ ax_1(t) $ is $ ay_1(t) $, where a is any complex constant.
Example for a linear system is
$ x_1 $ = 8$ e^t $
$ x_2 $=8$ t^2 $
Let ,
$ x_3 $ = 8$ e^t $ + 8$ t^2 $
