12.3. Basic Inverse Laplace Transforms

Try these first

1. 1.

   Find the inverse Laplace transform of F(s) = 1/s.

   Hint

   Think of basic pairs.

2. 2.

   What is the inverse Laplace transform of F(s) = 1/s^2?

   Hint

   Consider the function and derivatives.

3. 3.

   What is the inverse Laplace transform of F(s) = 1/s?

   • 1
   • t
   • e^{-t}

   Hint

   Refer to fundamental pairs.

4. 4.

   True or False: The Convolution Theorem can be applied to find the inverse of a product of Laplace transforms.

   • True
   • False

   Hint

   Consider the meaning of convolution.

5. 5.

   Derive the inverse Laplace transform of F(s) = (2s + 3)/(s^2 + 4). Use multiple methods.

   Hint

   Split into fractions to simplify the function.

6. 6.

   Using the Convolution Theorem, calculate the response function for the product of two transforms.

   Hint

   Keep track of limits and ensure correct integration.