Lecture 5.pdf

# Lecture 5.pdf - Laplace Transform Lecture 5 20-Feb-17 ME...

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Laplace Transform Lecture 5 20-Feb-17 ME 413: System Dynamics and Control: Dr Tesleem Asafa 1

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Differential equations: Linear Linear, time invariant Linear, time variant Which of these system is time invariant? Is independent variable order one Is coefficient a function of t? The most important property of linear systems is that the principle of superposition is applicable. 20-Feb-17 ME 413: System Dynamics and Control: Dr Tesleem Asafa 2
SOLVING LINEAR, TIME-INVARIANT DIFFERENTIAL EQUATIONS Two basic steps: By taking the Laplace transform of each term in the given differential equation, convert the differential equation into an algebraic equation in s and obtain the expression for the Laplace transform of the dependent variable by rearranging the algebraic equation. The time solution of the differential equation is obtained by finding the inverse Laplace transform of the dependent variable. 20-Feb-17 ME 413: System Dynamics and Control: Dr Tesleem Asafa 3

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Recall: The eq. becomes:

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