Duhamel's Principle

Find homogenous solution

Solve for , using the Laplace Transform

where is the Convolution of and

• is called the Forced Response
  • It is the solution that arises with the forcing function
  • It typically describes the steady-state behavior of the system
• is called the Natural Response
  • It is the solution that arises as a result of just the internal dyanmics of the system.
  • In a stable system, the natural response decays to zero, so it is also called the Transient Response