Determine the Laplace transform of f(t)={(t,text( if ) 0<t<2),(8-3t, text( if ) 2 <=t<3),(t-4,text( if ) 3 <=t<=4),(0, text( if ) 4<t):}

driliwra7 2022-09-12 Answered
Determine the Laplace transform of
f ( t ) = { t , if  0 < t < 2 8 3 t , if  2 t < 3 t 4 , if  3 t 4 0 , if  4 < t
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Answers (1)

Illuddybopylu
Answered 2022-09-13 Author has 17 answers
Hint: If
f ( t ) = { f 1 ( t ) 0 t < c 1 , f 2 ( t ) c 1 t < c 2 , f 3 ( t ) c 2 t < c 3 , f n 1 ( t ) c n 2 t < c n 1 , f n ( t ) t c n 1 .
then
f = f 1 + u c 1 ( f 2 f 1 ) + u c 2 ( f 3 f 2 ) + + u c n 1 ( f n f n 1 )
where u c ( t ) is step function.
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