10.7. Summary

Try these first

1. 1.

   What is the definition of the Dirac Delta Function?

   Hint

   Think about what happens during a sudden spike.

2. 2.

   What is the Laplace Transform of δ(t)?

   Hint

   Consider what happens at time t = 0.

3. 3.

   What does the Dirac Delta Function represent?

   • Continuous function
   • Instantaneous impulse
   • Constant function

   Hint

   Think of sudden spikes in a graph.

4. 4.

   True or False: The Laplace Transform of δ(t) is zero.

   • True
   • False

   Hint

   Consider results from specific time instances.

5. 5.

   Consider the system described by the equation d^2y/dt^2 + y = δ(t - 1). Solve for y(t).

   Hint

   Don't forget to utilize inverse transforms appropriately.

6. 6.

   Given an electrical circuit responding to δ(t) with a transfer function of H(s) = 1/(s+2), determine the output response for a δ(t - 4) input.

   Hint

   Focus on the relation from Laplace to time domain.