11.2. Definition of Periodic Functions

Try these first

1. 1.

   What is a periodic function?

   Hint

   Look for the definition of periodicity in the notes.

2. 2.

   Give an example of a periodic function.

   Hint

   Think about functions you know that are cyclic.

3. 3.

   Which of the following is a periodic function?

   • f(t) = e^t
   • f(t) = sin(t)
   • f(t) = ln(t)

   Hint

   Recall the definition of periodicity.

4. 4.

   True or False: The Laplace Transform can only be applied to continuous functions.

   • True
   • False

   Hint

   Remember the requirements discussed in class.

5. 5.

   Given a function f(t) that defines a triangular wave, derive its Laplace Transform.

   Hint

   Think about how to break the wave into segments for piecewise continuity.

6. 6.

   Explain how the understanding of periodic functions can help in improving control systems.

   Hint

   Consider how feedback loops utilize repetitive signals.