Find the inverse Laplace transform ccL^(-1){(s)/((s+1)^2−4)}.

dizxindlert7 2022-09-11 Answered
Find the inverse Laplace transform L 1 { s ( s + 1 ) 2 4 }
My textbook says that the solution is e t cosh ( 2 t ) 1 2 e t sinh ( t )
You can still ask an expert for help

Want to know more about Laplace transform?

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (2)

Maggie Tanner
Answered 2022-09-12 Author has 18 answers
Hint:
s ( s + 1 ) 2 2 2 = s ( s 1 ) ( s + 3 ) = 1 4 ( s 1 ) + 3 4 ( s + 3 ) ,
and
L ( e a t ) = 1 s a .
For the textbook solution, it is useful to write the given fraction as
s ( s + 1 ) 2 2 2 = s + 1 1 ( s + 1 ) 2 2 2 = s + 1 ( s + 1 ) 2 2 2 1 2 2 ( s + 1 ) 2 2 2 ,
and note that
L ( e a t cosh ( b t ) ) = s + a ( s + a ) 2 b 2 ,
and
L ( e a t sinh ( b t ) ) = b ( s + a ) 2 b 2 .

We have step-by-step solutions for your answer!

Leroy Gray
Answered 2022-09-13 Author has 3 answers
L 1 { s ( s + 1 ) 2 4 }
= L 1 { s + 1 ( s + 1 ) 2 4 } L 1 { 1 ( s + 1 ) 2 4 }
= e t cosh ( 2 t ) 1 2 e t sinh ( 2 t )

We have step-by-step solutions for your answer!

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

New questions