12. Laplace Transforms & Applications

Try these first

1. 1.

   What is L^{-1}{1/s}?

   Hint

   This is a basic transformation.

2. 2.

   What is L^{-1}{1/s^2}?

   Hint

   This is the second basic inverse transform.

3. 3.

   What does the Inverse Laplace Transform retrieve?

   • Frequency-domain functions
   • Time-domain functions
   • Complex functions

   Hint

   Think about what transformation we are reversing.

4. 4.

   True or False: The Convolution Theorem is used when dealing with the product of Laplace transforms.

   • True
   • False

   Hint

   Recall how convolution integrates two functions.

5. 5.

   Given the differential equation y'' + 4y = 0 with initial conditions y(0) = 1, y'(0) = 0, find y(t) using the Laplace Transform method.

   Hint

   Identify the initial conditions properly while transforming.

6. 6.

   Use the convolution theorem to find L^{-1}{(1/(s+1))(1/(s+2))}.

   Hint

   Focus on breaking down the functions first.