What is the Laplace Transform of f(t)=u(sin(2t))?

Iyana Jackson

Iyana Jackson

Answered question

2022-09-08

What is the Laplace Transform of f ( t ) = u ( sin ( 2 t ) )?
I'm confused how to proceed further? because u(t)=0 for t<0. What does having sin ( 2 t ) in argument mean?

Answer & Explanation

Krista Leon

Krista Leon

Beginner2022-09-09Added 12 answers

If u(t)=1 for positive t, and 0 otherwise, then u ( sin ( 2 t ) ) = 1 whenever sin ( 2 t ) is positive.
That is, f ( t ) = 1 whenever 2 t is in one of the intervals ( 0 , π ) , ( 2 π , 3 π ) , ( 4 π , 5 π ) , ( 2 π , π ) ,
meaning t is in one of the intervals ( 0 , π 2 ) , ( π , 3 π 2 ) , ( 2 π , 5 π 2 ) , ( π , π 2 ) ,
and f ( t ) = 0 otherwise. This is a square wave.

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