2.2. Definition of Laplace Transform

Try these first

1. 1.

   Find the Laplace Transform of f(t) = 5.

   Hint

   Use the basic Laplace Transform rule.

2. 2.

   What is the Laplace Transform of sin(t)?

   Hint

   Refer to the known formula for sin.

3. 3.

   What does the Laplace Transform do?

   • Transforms time-domain functions to frequency-domain functions
   • Increases complexity
   • Solves equations directly

   Hint

   Think about the benefits it provides in solving equations.

4. 4.

   True or False: The Laplace Transform of a sum of functions is equal to the sum of their individual Laplace Transforms.

   • True
   • False

   Hint

   Recall the definition of linearity in mathematics.

5. 5.

   A function f(t) = 5t^3 - 4cos(3t) + 2e^(-2t) is given. What is its Laplace Transform?

   Hint

   Break down each component and use the respective formulas.

6. 6.

   If f(t) = t*sin(t) + e^(3t) + 6, what is its Laplace Transform?

   Hint

   You’ll need to apply integration by parts for the first term.