12.13. Laplace Transform of Dirac Delta Function

Try these first

1. 1.

   What is the Laplace transform of δ(t−a)?

   Hint

   Consider how instant forces are represented.

2. 2.

   Why is the Dirac delta function important in engineering?

   Hint

   Think about point sources in structures.

3. 3.

   What is the Laplace transform of δ(t−a)?

   • e^(-as)
   • a^(-t)
   • δ(t-a)
   • 0

   Hint

   Focus on the time shift in the delta function.

4. 4.

   True or False: The Dirac delta function can model forces that act over a duration.

   • True
   • False

   Hint

   Think about how it behaves at a point.

5. 5.

   How would the Laplace transform of a system change if instead of an ideal impulse, we had a finite duration pulse? Provide the transformation.

   Hint

   Look deeper into how the finite pulse affects the integral.

6. 6.

   Critique the assumption of using the Dirac delta function in numerical simulations. How could approximating it lead to complications?

   Hint

   Consider numerical methods for approximating impulses.