9.1.4. 7. Properties Involving Unit Step

Try these first

1. 1.

   What is the definition of the unit step function?

   Hint

   Think about how this function activates at a certain point.

2. 2.

   Write down the formula for the Laplace Transform of a unit step function.

   Hint

   Look at the standard results section in your notes.

3. 3.

   What is the main property of the unit step function?

   • It is continuous everywhere
   • It is zero before a certain time and one afterwards
   • It oscillates between -1 and 1

   Hint

   Think about its definition.

4. 4.

   True or False: The Laplace Transform preserves the linearity property.

   • True
   • False

   Hint

   Consider how we can add transforms.

5. 5.

   Given the function f(t) = 3(t-4)u(t-4), derive the Laplace Transform.

   Hint

   Use integration by parts along with the second shifting theorem.

6. 6.

   Design a model for a mechanical system where a unit step function is critical. Explain how you would apply Laplace Transforms in this model.

   Hint

   What happens to the system when the force is suddenly applied?