How to find the Laplace transformation L{cos(8t) sqrt(t/(pi))}?

Sasha Hess 2022-09-11 Answered
Given L { cos ( 8 t ) / π t } = e 8 / s / s
How to find the Laplace transformation
L { cos ( 8 t ) t / π }?
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Answers (1)

Aldo Harrington
Answered 2022-09-12 Author has 12 answers
L { cos 4 2 t π t u ( t ) } = e 8 / s s .
Since
t cos 4 2 t π = cos 4 2 t π t t ,
Integrating-by-parts Laplace transform of t f ( t ) is L { f ( t ) }
We have:
L { t cos 4 2 t π u ( t ) } = d d s L { cos 4 2 t π t u ( t ) } = d d s e 8 / s s = e 8 / s ( s 16 ) 2 s 5 / 2 .

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