What is the laplace transform of the following function f(t)=t^(10) cosh (t)

katdoringlo

katdoringlo

Answered question

2022-09-12

What is the laplace transform of the following function
f ( t ) = t 10 cosh ( t )
Is there another method that doesn't include differentiating the Laplace transform of cosh t ten times?

Answer & Explanation

Hajdiniax

Hajdiniax

Beginner2022-09-13Added 8 answers

f ( t ) = t 10 cosh t = t 10 ( e t + e t 2 ) = 1 2 t 10 e t + 1 2 t 10 e t L ( f ( t ) ) = 1 2 10 ! ( s 1 ) 11 + 1 2 10 ! ( s + 1 ) 11
tophergopher3wo

tophergopher3wo

Beginner2022-09-14Added 5 answers

Yes. Remember that cosh ( t ) = e t + e t 2 . Use this to rewrite f(t) and use a relatively simple Laplace transform for functions of the form t n e a t

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