10.2.2. Special Case: δ(t)

Try these first

1. 1.

   What does the Dirac Delta Function model?

   Hint

   Think about sudden changes.

2. 2.

   What is the value of the Laplace Transform of δ(t)?

   Hint

   Consider what happens when a = 0.

3. 3.

   What is the value of the Laplace Transform of δ(t - 2)?

   • e^(-2s)
   • 1
   • 0

   Hint

   Think of the general formula for the delta function.

4. 4.

   True or False: The Dirac Delta Function can be considered a true function.

   • True
   • False

   Hint

   Consider its behavior at points of interest.

5. 5.

   Prove the Laplace Transform of δ(t) using integration.

   Hint

   Start from the definition of the Laplace Transform.

6. 6.

   Using a system described by dy/dt + 2y = δ(t - 3), solve for y(t) using the Laplace Transform.

   Hint

   Use the shifting property and remember to apply inverse transformations.