One definition for a function ft ft0 for t0

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ls in the course! One Definition: For a function f(t) (f(t)=0 for t<0), Definition: We can transform an ordinary differential We equation (ODE) into an algebraic equation (AE). t-domain (s: complex variable) s-domain AE ODE 1 f(t) 2 0 t F(s) Solution to ODE We denote Laplace transform of f(t) by F(s). We 3 3 Partial fraction expansion 4 Properties of Laplace transform Differentiation (review) Example 1 ODE with initial conditions (ICs) t-domain 1. Laplace transform s-domain 5 Example 1 (cont’d) 2. Partial fraction expansion 6 Example 1 (cont’d) unknowns 3. Inverse Laplace transform Multiply both sides by s & let s go to zero: Similarly, If we are interested in only the final value of y(t), apply y(t), Final Value Theorem: 7 8 Example 2 S1 S1 In this way, we can find a rather complicated solution to ODEs easily by using Laplace transform table...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online