Laplace Transform of multiplied term like u(t)u(4−t)

kasibug1v 2022-10-05 Answered
Laplace Transform of multiplied term like u ( t ) u ( 4 t )
First of all,
If this is a two-terms function I'd be simple. It will produce
L [ u ( t ) ] = 1 s
Except, I'm not sure what to do with u ( 4 t ). If it was u ( t 4 ), it would be simpler.
Secondly,
Since these two terms are not separate. I couldn't find a property to help me deal with it.
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Answers (1)

farbhas3t
Answered 2022-10-06 Author has 6 answers
I think the easiest way is to use the definition of the Laplace transform directly. Note that
u ( t ) u ( 4 t ) = { 1 , 0 < t < 4 0 , otherwise ,
so
L [ u ( t ) u ( 4 t ) ] ( s ) = 0 4 e s t d t ,
which I am sure you can work out.
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