17.4. Theoretical Framework

Try these first

1. 1.

   What is the purpose of the Laplace Transform?

   Hint

   What does it simplify?

2. 2.

   What do we apply at the beginning when solving using Laplace Transforms?

   Hint

   What do you turn the equations into?

3. 3.

   What is the first step in solving simultaneous linear differential equations using Laplace Transforms?

   • Take derivatives
   • Take Laplace Transforms
   • Use initial conditions

   Hint

   What do we transform to simplify them?

4. 4.

   True or False: The Inverse Laplace Transform is used to return solutions to the time domain.

   • True
   • False

   Hint

   What do we need for practical applications?

5. 5.

   Given these two equations, dx/dt = 2x + 3y, dy/dt = -y + 4x, apply Laplace Transforms and find the solution for x(t) and y(t).

   Hint

   Use initial conditions and manipulate equations after the transform.

6. 6.

   Explain how a non-linear system might differ in approach when applying Laplace Transforms.

   Hint

   Consider how linearity affects the math behind the transforms.