Is it possible to rewrite Lf(t+a), where a is some arbitrary constant, to have an expression involving F?

Gauge Odom

Gauge Odom

Answered question

2022-09-09

Typical notation for Laplace transforms is that L f ( t ) = F ( s )
Is it possible to rewrite L f ( t + a ), where a is some arbitrary constant, to have an expression involving F?

Answer & Explanation

Andrejkoxg

Andrejkoxg

Beginner2022-09-10Added 20 answers

L ( f ( t ) ) = 0 f ( t ) e s t   d t = F ( s ). So
L ( f ( t + a ) ) = 0 f ( t + a ) e s t   d t = a f ( p ) e s ( p a )   d p = e a s [ F ( s ) 0 a f ( p ) e s p   d p ]

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