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Laplace Transform

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Respect (73%):
Date Posted: 5/16/2008 10:34:34 AM  Status: Live
Laplace Transform
Course Textbook Chapter Problem
Calculus N/A N/A N/A
Question Details:
use the operational properties of the Laplace transform and the Basic Table to determine the Laplace transform of the following  function
 
   f(t) = e-t sin2t

Answers:

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Sage
Karma Points: 5,119
Date Posted: 5/16/2008 10:57:29 AM  Status: Live
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Response:
Not sure what transforms are on your basic table, but using these three and two properties
[1]
[2]
[3]
[P1]
[P2]



Using [1]


Taking f(t) to be sin2(t)



So we can take the Laplace transform of sin2 t and "evaluate" at s+1.  Since sin2t, is not likely to be on the table, we can use the identity sin2t = 1/2 [1-cos(2t)].


Using the linear property of the transform [P1] and [P2]


Using [2] and [3] from the table



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