12.5. Applications of Inverse Laplace Transform

Try these first

1. 1.

   What does the Inverse Laplace Transform do?

   Hint

   Think about converting from frequency to time domain.

2. 2.

   What is the ILT of 1/s²?

   Hint

   Consider the basic pair for your reference.

3. 3.

   What is the main purpose of the Inverse Laplace Transform?

   • To convert functions back to time domain.
   • To differentiate functions.
   • To integrate functions.

   Hint

   Consider what transformation you perform after the Laplace Transform.

4. 4.

   True or False: The Convolution Theorem is used to compute the ILT of a sum of functions.

   • True
   • False

   Hint

   Focus on the operations involved with the theorem.

5. 5.

   Given F(s)=2/(s^2+4), use the Partial Fraction Method to find L−1{F(s)}.

   Hint

   Be cautious with the coefficients and factoring.

6. 6.

   Using the Convolution Theorem, find the inverse Laplace of F(s) = (s+1)/(s^2+1)(s^2+4).

   Hint

   Remember to integrate the product of the ILTs.