2. This problem will show you how to derive a formula for L{cos(bt)} without directly evaluating the integral by using the identity eta = cos(a) + i sin(a). a. Use the above identity to show that - elbt te-ibt 2 = cos(bt). b. Use the identity from part a and the linearity of the Laplace transform to evaluate L{cos(at)}. Make sure it agrees with what is shown in the table.
2. This problem will show you how to derive a formula for L{cos(bt)} without directly evaluating the integral by using the identity eta = cos(a) + i sin(a). a. Use the above identity to show that - elbt te-ibt 2 = cos(bt). b. Use the identity from part a and the linearity of the Laplace transform to evaluate L{cos(at)}. Make sure it agrees with what is shown in the table.
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
![2. This problem will show you how to derive a formula for £{cos(bt)} without directly
evaluating the integral by using the identity eia = cos(a) + i sin(a).
eibt +e-ibt
a.
Use the above identity to show that-
=
cos (bt).
2
b.
Use the identity from part a and the linearity of the Laplace transform to
evaluate L{cos(at)}. Make sure it agrees with what is shown in the table.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F21e98448-8eaa-4c09-a4ab-b543c4300c00%2F18251e3f-2011-4b61-8ba2-e163659772f5%2Fxfeh9be_processed.png&w=3840&q=75)
Transcribed Image Text:2. This problem will show you how to derive a formula for £{cos(bt)} without directly
evaluating the integral by using the identity eia = cos(a) + i sin(a).
eibt +e-ibt
a.
Use the above identity to show that-
=
cos (bt).
2
b.
Use the identity from part a and the linearity of the Laplace transform to
evaluate L{cos(at)}. Make sure it agrees with what is shown in the table.
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