Need to find the Laplace transform of the following function 1/4 tu(t−7) using the second shifting theorem

tamola7f

tamola7f

Answered question

2022-09-11

I need to find the Laplace transform of the following function 14tu(t−7) using the second shifting theorem
My working is as follows
1 4 t u ( t 7 ) = e 7 s L ( 1 4 ( t + 7 ) )
= e 7 s ( 1 4 s 2 + 7 4 s )
Is this correct?

Answer & Explanation

Jazmin Bryan

Jazmin Bryan

Beginner2022-09-12Added 12 answers

f ( t ) = 1 4 t u ( t 7 )
Rewrite it as:
f ( t ) = 1 4 ( ( t 7 ) u ( t 7 ) + 7 u ( t 7 ) )
f ( t ) = 1 4 ( t 7 ) u ( t 7 ) + 7 4 u ( t 7 )
Apply the Shift Theorem.
F ( s ) = e 7 s 4 s 2 + 7 e 7 s 4 s
F ( s ) = e 7 s 4 s ( 1 s + 7 )

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