1.3. First Shifting Theorem (Laplace Domain Shift)

Try these first

1. 1.

   Find the Laplace Transform of e^(2t) using the First Shifting Theorem.

   Hint

   Start with the base transform of a constant.

2. 2.

   What happens to the Laplace Transform if f(t) = e^(3t) multiplied by t?

   Hint

   Look at the basic transformation of t.

3. 3.

   What is the result of applying the First Shifting Theorem to e^(2t)sin(bt)?

   • (s-2)^2 + b^2
   • s^2 + b^2
   • s + 2 + b

   Hint

   Look at how multiplication affects the Laplace domain.

4. 4.

   True or False: The First Shifting Theorem applies only to polynomial functions.

   • True
   • False

   Hint

   Think about all types of functions affected by the theorem.

5. 5.

   Find the Laplace Transform of the function e^(5t) * cos(3t).

   Hint

   Start with the basic transform of cos(3t) and adjust for the shifting.

6. 6.

   Use the First Shifting Theorem to find the Laplace Transform of e^(-t) * e^(2t).

   Hint

   Deal with each exponential term before applying the theorem.