rhenan5v

rhenan5v

Answered

2022-10-26

How to Find Inverse Laplace Transform of F ( s ) = 1 π cot 1 ( 10 s π )

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Answer & Explanation

Adenomacu

Adenomacu

Expert

2022-10-27Added 13 answers

Hint:
π t f ( t ) = L 1 ( d d s cot 1 ( 10 s / π ) )

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Paloma Sanford

Paloma Sanford

Expert

2022-10-28Added 3 answers

We know :
c o t 1 ( x ) = π 2 t a n 1 ( x )
So :
F ( s ) = c o t 1 ( 10 s π ) π = 1 π ( π 2 t a n 1 ( 10 s π ) )
Also we know :
L [ t f ( t ) ] = d d s F ( s )
So :
d d s F ( s ) = 1 π [ 10 π ( 10 π ) 2 s 2 + 1 ] = ( 1 π ) ( π 10 ) s 2 + ( π 10 ) 2
L 1 [ d d s F ( s ) ] = t f ( t )
t f ( t ) = 1 π s i n ( π 10 t )
f ( t ) = s i n ( π t 10 ) π t

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