Lecture Notes (3)

# One definition for a function ft ft0 for t0

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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...
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## This document was uploaded on 03/02/2014 for the course ME 451 at Michigan State University.

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