9.1.2. Standard Result

Try these first

1. 1.

   What is the value of u(t-5) when t = 3?

   Hint

   Think about the definition of the unit step function.

2. 2.

   Write the expression for the Laplace Transform of u(t-4).

   Hint

   Consider the standard result we've just discussed.

3. 3.

   What does the unit step function u(t-a) equal for t < a?

   • 0
   • 1
   • Undefined

   Hint

   Recall the definition of the unit step function.

4. 4.

   The Laplace Transform of u(t-a) is which of the following?

   • \\( \\frac{e^{-as}}{s} \\)
   • \\( \\frac{a}{s} \\)
   • s

   Hint

   Consider the formula discussed in class.

5. 5.

   Derive the Laplace Transform of the function f(t) = (3t + 2)u(t-1). What is the transformed function?

   Hint

   Break it down, and remember to apply the theorem after recognizing the step function.

6. 6.

   Model a mechanical system experiencing a sudden force at t = 5 seconds. Write the governing differential equation and solve using Laplace Transform.

   Hint

   Apply the Laplace Transform for each term, recalling initial conditions.