The-Laplace-Transfor-new.docx - Contents 1 The Laplace

The-Laplace-Transfor-new.docx - Contents 1 The Laplace

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Contents 1. The Laplace Transform ………………………………………………………………………………………..….…….…2 1.1 Definition………………………………………………………….…………..……………………….…….…..…2 2. Simple Mass-Spring System in Free Vibration ……………………………………..……………...…...……3 . 2.1. In the cases of simple Mass-Spring systems…………………………………………..…………..3 2.2. Simple Damped Mass-Spring Systems in Free Vibration………………………………...……4 2.3. Sources of Damping in Mechanical Vibrations…………………………………..…………..…….4 2.4. Physical model of Damped Mass-Spring Systems in Free Vibration……..……..…….…5 2.5. Physical modeling of Damped Mass-Spring Systems in Free Vibration…………….…...5 2.6. Mathematical modeling of Damped Mass-Spring Systems in Free Vibration…..…….6 3.Applying the Laplace Transforms to Solve Differential Equations ……………………..…… ......... 7 3.1 Solving for Y(s)……………………………….……………………………………………………………….… .... 8 4. Damping Mass in a Motorcycle suspension system …………………………………………….…………8 4.1. Specific Case…………………………………………………………………………………….…….……..…….8 4.2. Solution to Y(t) – Inverse Laplace Transform………………………………………..…..…………10 5.The Damping Ratio ………………………………………………………………………………………………………….11 5.1. Definition………………………………………………………………………………………………………….11 5.2.Derivation……………………………………………………………………………………………………………12 5.3. Damping Mass in a Motorcycle Suspension…………………………………………………………13 6.Conclusion ………………………………………………………………………………………………………………………14 7.References ………………………………………………………………………………………………………………………14 1
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1.The Laplace Transform: 1.1 Definition: The ability to obtain linear approximations of physical systems allows the analyst to consider the use of the Laplace transformations mentioned in our introduction. The Laplace transform allows us to take a complex differential
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