Inverse Laplace Transforms (ILT) 3 basic cases Distinct poles Repeated poles Complex conjugate poles

Basic facts/techniques that YOU will use Partial Fraction Expansion (PFE) ALGEBRA You must use my approach.

Preliminary Example

Partial Fraction Expansion Factor denominator into linear factors with coefficient of s being 1 in each factor. Break up big fraction into sum of simple fractions (Partial fractions) with linear denominator. Use formulas to ILT each term (terms are ADDED together, factors are multiplied) Use algebra to simplify (get rid of j’s)

Example 1

“Cover up rule” Choose a denominator Multiply both sides by denominator Evaluate both sides at the s that makes the denominator 0. Only numerator over chosen denominator survives. Choose next denominator, etc. You MUST USE COVER UP RULE

Example 2

Example 3

ILT, PFE, Cover up Rule distinct roots, multiple roots Real roots, complex conjugate pairs of roots Expect a 3rd or 4th order test problem Calculator only used to find roots of denominators Going from roots to factors Show all work, No work  No credit