11.4. Derivation

Try these first

1. 1.

   What is a periodic function?

   Hint

   Think of sine and cosine functions.

2. 2.

   State the formula for the Laplace Transform of a periodic function.

   Hint

   Look for one part of the formula related to the period T.

3. 3.

   What type of function is f(t) if it satisfies f(t + T) = f(t)?

   • Exponential Function
   • Periodic Function
   • Linear Function

   Hint

   Recall the definition of periodic functions.

4. 4.

   The Laplace Transform allows us to analyze what type of systems?

   • True
   • False

   Hint

   Consider if it’s applicable across engineering disciplines.

5. 5.

   Derive the Laplace Transform of a custom defined periodic function f(t) = sin(t) + cos(t) for 0 ≤ t < T.

   Hint

   Ensure to consider the periodic conditions during integration.

6. 6.

   Explain how the Laplace Transform can change when the periodic function is modified, such as changing amplitude or frequency.

   Hint

   Think about how physical systems respond to frequency changes.