6) Use the definition of the Laplace transform, F(t) = | f(t) e*"dt , to find L{sin kt} . Compare how the calculation of the Laplace transform of sin 2t was shown in the book. -e-s sin 2t L{sin 2r) e sin 2r dt = e-s cos 2t dt %3D es cos 2t dt, s >0. %3D lim e cos 2r 0, s >0 Laplace transform of sin 21 -e-st cos 2t es sin 21 dt 4. L{sin 2r). %3D At this point we have an equaion with L{sin 21) on both sides of the equality. Solving for that quantity yields the result 2 L sin 21) =- s>0, +4 DO NOT copy this solution with 2 replaced by k. It leaves out too many steps. Your job is to make the calculation of L{sin kt} understandable. Show the steps as done in class including the integration by parts by the tabular method and the calculation of the improper integrals. I.

6) Use the definition of the Laplace transform, F(t) = | f(t) e*"dt , to find L{sin kt} . Compare how the calculation of the Laplace transform of sin 2t was shown in the book. -e-s sin 2t L{sin 2r) e sin 2r dt = e-s cos 2t dt %3D es cos 2t dt, s >0. %3D lim e cos 2r 0, s >0 Laplace transform of sin 21 -e-st cos 2t es sin 21 dt 4. L{sin 2r). %3D At this point we have an equaion with L{sin 21) on both sides of the equality. Solving for that quantity yields the result 2 L sin 21) =- s>0, +4 DO NOT copy this solution with 2 replaced by k. It leaves out too many steps. Your job is to make the calculation of L{sin kt} understandable. Show the steps as done in class including the integration by parts by the tabular method and the calculation of the improper integrals. I.

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

6) Use the definition of the Laplace transform, F(t) = f)e"dt, to find L{sin kt} .
Compare how the calculation of the Laplace transform of sin 2t was shown in the book.
-e-st sin 2t
L{sin 2r)
e sin 2r dt =
est cos 2t dt
%3D
一
e cos 2t dt,
s >0.
%3D
lim e
cos 2r 0, s >0
Laplace transform of sin 2r
-est cos 2t
est sin 2r dt
4.
L{sin 2r}.
At this point we have an equaion with L{sin 21) on both sides of the equality.
Solving for that quantity yields the result
2
L sin 2) =
s>0,
DO NOT copy this solution with 2 replaced by k. It leaves out too many steps.
Your job is to make the calculation of L{sin kt} understandable.
Show the steps as done in class including the integration by parts by the tabular method and
the calculation of the improper integrals.
I.

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