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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