11. Laplace Transform of Periodic Functions

Try these first

1. 1.

   Define a periodic function.

   Hint

   Think about functions that repeat over intervals.

2. 2.

   What is the period T of the function f(t)=sin(t)?

   Hint

   Identify how frequently the sine function completes a cycle.

3. 3.

   What is the period of the function f(t)=cos(t)?

   • π
   • 2π
   • 3π

   Hint

   Consider the unit circle and how cosine relates to angle.

4. 4.

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

   • True
   • False

   Hint

   Think about functions that might not be fully continuous but still usable.

5. 5.

   Given a periodic triangular wave defined as f(t) = |t mod T|, derive the Laplace Transform.

   Hint

   Focus on breaking the function appropriately to ease integration.

6. 6.

   Analyze a complex engineering system where a periodic input is defined. How would you calculate the effective system response using the Laplace Transform?

   Hint

   Identify the periodicity and effectively apply the theorem.