Find: Using complex integration, prove the inverse Laplace transform of F(s) is sin(2t) L-¹ [F(s)] = 1
Find: Using complex integration, prove the inverse Laplace transform of F(s) is sin(2t) L-¹ [F(s)] = 1
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
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![Given: There is a table of Laplace transform pairs on page 249 of the course text. Item 13 shows
that
1
s²+w²
Suppose you have some transformed function, F(s), where
1
s² + 4
Find: Using complex integration, prove the inverse Laplace transform of F(s) is
L-1
F(s) =
=
1
=
sin wt
L-¹ [F(s)]==sin(2t)
Recall, the inverse Laplace transform is defined as
potico
1
f(t) = L-¹ [F(s)] = 27, ***** F(s)eªds
Jo-100
Note o is a constant value.
Hint: Apply residue integration-the key is to pick a contour that encircles the poles AND ensures
the added part of the contour goes to zero.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd48b8819-fa93-4be0-8e21-0a11df5ef5a7%2Faa87ca82-392f-4f03-b29c-07f4658b32e9%2F7ciwjcs_processed.png&w=3840&q=75)
Transcribed Image Text:Given: There is a table of Laplace transform pairs on page 249 of the course text. Item 13 shows
that
1
s²+w²
Suppose you have some transformed function, F(s), where
1
s² + 4
Find: Using complex integration, prove the inverse Laplace transform of F(s) is
L-1
F(s) =
=
1
=
sin wt
L-¹ [F(s)]==sin(2t)
Recall, the inverse Laplace transform is defined as
potico
1
f(t) = L-¹ [F(s)] = 27, ***** F(s)eªds
Jo-100
Note o is a constant value.
Hint: Apply residue integration-the key is to pick a contour that encircles the poles AND ensures
the added part of the contour goes to zero.
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