17.2. Introduction

Try these first

1. 1.

   What is the purpose of the Laplace Transform?

   Hint

   Think about why algebraic equations are easier to deal with.

2. 2.

   Name one application for simultaneous linear differential equations.

   Hint

   Consider where these equations frequently arise in technology.

3. 3.

   What does the Laplace Transform simplify?

   • Differential equations into algebraic equations
   • Complex numbers into real numbers
   • The need for calculus

   Hint

   Think about the main goal of using Laplace Transforms.

4. 4.

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

   • True
   • False

   Hint

   Consider what happens after you transform the equations.

5. 5.

   Given the simultaneous equations dx/dt = 5x + 3y and dy/dt = 2x + 4y, apply the Laplace Transform and find the solutions in the time domain.

   Hint

   Use the initial conditions for x(0) and y(0) if provided.

6. 6.

   Consider a mechanical system defined by dx/dt = 7x + 2y, dy/dt = -5x + 6y. Show how to apply the Laplace Transform and find the time functions.

   Hint

   Don’t forget to arrange the equations in proper form to utilize substitution!