MECH 466 - Lecture3-ODEs-2009W

Partial fraction expansion example 2 contd unknowns 2

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Unformatted text preview: e 2 (cont’d) unknowns 2. Partial fraction expansion To obtain A: unknowns To obtain C: To obtain B: Take derivative Let s go to -2. 2008/09 MECH466 : Automatic Control 13 2008/09 MECH466 : Automatic Control 14 Properties of Laplace transform 8. Frequency shift theorem (review) Example 2 (cont’d) 3. Inverse Laplace transform t-domain Proof. s-domain If we are interested in only the final value of y(t), apply y(t), Final Value Theorem: 2008/09 MECH466 : Automatic Control Ex. 15 2008/09 MECH466 : Automatic Control 16 4 Example 3 (complex roots) Example 3 (cont’d) ODE with zero initial conditions (ICs) unknowns 2. Partial fraction expansion 1. Laplace transform To obtain A, B & C: Complex roots 2008/09 MECH466 : Automatic Control 17 2008/09 Example 3 (cont’d) MECH466 : Automatic Control 18 Example: Newton’s law 3. Inverse Laplace transform M We want to know the trajectory...
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This document was uploaded on 03/05/2014 for the course MECH 466 at The University of British Columbia.

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