6.6. Example Problems

Try these first

1. 1.

   What is the Laplace Transform of sin(at)?

   Hint

   Think about the standard transformation for sin functions.

2. 2.

   State the integral relationship for Laplace Transform.

   Hint

   Recall how integrating affects the transform.

3. 3.

   What is the formula for the Laplace Transform of an integral of a function?

   • F(s) / s
   • F(s) * s
   • F(s) + s

   Hint

   Recall the theorem we just discussed.

4. 4.

   Is the Laplace Transform useful for solving differential equations in engineering?

   • True
   • False

   Hint

   Think about its application in circuit analysis.

5. 5.

   Discuss the limitations of using Laplace Transforms in certain types of engineering problems. What could be problematic?

   Hint

   Think about what kinds of functions might cause trouble.

6. 6.

   Find the Laplace Transform of the integral of a unit step function u(t) from 0 to t.

   Hint

   Remember how unit step functions behave.