Differential Equations : The Laplace Transform

Example Questions

Example Question #1 : Definition Of Laplace Transform

Find the Laplace Transform for the following function.

Explanation:

To find the Laplace Transform for the following function

use the transforms for basic functions which state,

Example Question #1 : Transforms Of Periodic Functions

Find the Laplace transform of the periodic function.

Explanation:

This particular piecewise function is called a square wave. The period of this function is the length at which it takes the function to return to its starting point.

For this particular function

it has a period of

.

and furthermore,

Using the Transform of a Periodic Function Theorem which states,

the problem can be solved as follows.