10.2. Special Case: δ(t)

Try these first

1. 1.

   What is the value of δ(t−2) when t = 3?

   Hint

   Evaluate the condition where t does not equal 2.

2. 2.

   What is the integral of δ(t−1) from -∞ to +∞?

   Hint

   Recall the defining property of the Dirac Delta Function.

3. 3.

   What is the value of δ(t) when t = 0?

   • 0
   • ∞
   • 1

   Hint

   Think about the definition of the Dirac Delta Function.

4. 4.

   The Laplace Transform of δ(t−a) is equal to:

   • e^(-as)
   • 1
   • k * e^(-as)

   Hint

   Recall the formula we derived.

5. 5.

   Given the equation d^2y/dt^2 + 3dy/dt + 2y = δ(t−2), solve for y(t) and provide the solution using Laplace Transforms.

   Hint

   Break it down with impulse response considerations.

6. 6.

   A system is defined with L(s) = (2s + 3)/(s^2 + 5s + 6). How does this equation behave when an impulse input δ(t) is applied at multiple points?

   Hint

   Make sure to evaluate at each impulse point.