Determine the Laplace transform of f(t) below: f(t)={(0",",if t<2),((t-2)^2 ",", if t >=2):}

tikaj1x 2022-10-21 Answered
Determine the Laplace transform of f(t) below:
f ( t ) = { 0 , if  t < 2 ( t 2 ) 2 , if  t 2
So my answer is
2 e 2 s / s 3
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Answers (2)

Laci Conrad
Answered 2022-10-22 Author has 17 answers
With problems of this form, we can simplify the integration by recognizing the derivative.
2 ( t 2 ) 2 e s t d t = 2 t 2 e s t d t 4 2 t e s t d t + 4 2 e s t d t = 2 s 2 2 e s t d t + 4 s 2 e s t d t + 4 2 e s t d t = 2 s 2 e 2 s s + s 4 e 2 s s + 4 e 2 s s
From this, we obtain the answer
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duandaTed05
Answered 2022-10-23 Author has 6 answers
Given the Laplace transform as
f ( s ) = 0 e s t f ( t ) d t
then for
f ( t ) = { 0 , if  t < 2 ( t 2 ) 2 , if  t 2
it is seen that
f ( s ) = 0 2 e s t ( 0 ) d t + 2 e s t ( t 2 ) 2 d t = 0 + 0 e s ( u + 2 ) u 2 d u = 2 e 2 s s 3 .
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