Find the inverse Laplace transform for each of the following.a.b.1s² + 4s +132s+4[3²-2414]+ 4s

Answered: Find the inverse Laplace transform for…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Find the inverse Laplace transform for each of the following.
a.
b.
1
s² + 4s +13
2s+4
[3²-2414]
+ 4s

Expert Solution

Step 1: Introduction

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a) We have to find the inverse Laplace transform of the following function

$fraction numerator 1 over denominator s squared plus 4 s plus 13 end fraction$

We know that

$L to the power of negative 1 end exponent open curly brackets ϕ left parenthesis s plus a right parenthesis close curly brackets equals e to the power of negative a t end exponent L to the power of negative 1 end exponent open curly brackets ϕ open parentheses s close parentheses close curly brackets L to the power of negative 1 end exponent open curly brackets fraction numerator 1 over denominator s squared plus a squared end fraction close curly brackets equals fraction numerator sin a t over denominator a end fraction$