15.12. Laplace Transform of Piecewise and Discontinuous Functions

Try these first

1. 1.

   Define a unit step function.

   Hint

   Think about how the function reacts before and after a certain time.

2. 2.

   What is the transform of the unit step function?

   Hint

   Recall the equation we just discussed.

3. 3.

   What is the Laplace Transform of the unit step function?

   • e^{-as}/s
   • s/e^{as}
   • 0

   Hint

   Remember the definition of the unit step function.

4. 4.

   True or False: The shifted function allows for effective modeling of loads applied after a delay.

   • True
   • False

   Hint

   Think about when a load starts acting.

5. 5.

   Given a beam subjected to a point load that is instantly applied at t=3s and removed at t=6s, represent the load using a piecewise function and find its Laplace transform.

   Hint

   Look into how each piece of the load behaves at different times.

6. 6.

   Formulate and solve for the Laplace transform of the following piecewise function: f(t) = 10u(t-2) + 5u(t-4).

   Hint

   Break it down by examining each unit step function's contribution.