Differential Equations : Transforms of Periodic Functions

Study concepts, example questions & explanations for Differential Equations

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Example Questions

Example Question #2 : The Laplace Transform

Find the Laplace transform of the periodic function.

Possible Answers:

Correct answer:


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.

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