1.7. Graphical Representation

Try these first

1. 1.

   What is the formula for the Second Shifting Theorem?

   Hint

   Look for the exponential term associated with the delay.

2. 2.

   What does the Heaviside step function model?

   Hint

   Think about functions that start later than t=0.

3. 3.

   What does the Second Shifting Theorem apply to?

   • Only continuous functions
   • Delayed functions
   • Discrete functions

   Hint

   Think about what the theorem is designed to model.

4. 4.

   True or False: The Heaviside step function can activate functions before time zero.

   • True
   • False

   Hint

   Reflect on how the Heaviside function is structured.

5. 5.

   Use the Second Shifting Theorem to find the Laplace Transform of (t-3)³u(t-3). Explain each step.

   Hint

   Break it into f(t) and analyze how delays impact the equation.

6. 6.

   Create a piecewise function that incorporates Heaviside steps and compute its Laplace Transform.

   Hint

   Consider each part of the piecewise function separately for proper activation.