10.2.1. Definition

Try these first

1. 1.

   What is the value of δ(t - a) for t ≠ a?

   Hint

   Think about where the impulse occurs.

2. 2.

   What is the integral of δ(t - a) over all time?

   Hint

   Recall the defining property of the delta function.

3. 3.

   What is the Laplace Transform of δ(t)?

   • e^(−as)
   • 1
   • 0

   Hint

   Recall the special case of the delta function.

4. 4.

   True or False: The Dirac Delta Function is a standard function.

   • True
   • False

   Hint

   Think about its definition and properties.

5. 5.

   Given a system modeled by the differential equation d²y/dt² + 3dy/dt + 2y = δ(t - 1), find the particular solution.

   Hint

   Separate the terms and examine the role of the delta function.

6. 6.

   How would you formulate a system response if the input is δ(t - a) and state the implications?

   Hint

   Link the concepts of impulse response and system dynamics.