Question

Inverse Laplace transform of
\[\log(1+a^2/s^2 )\]

There is one property i am not recollecting.
I can differentiate the above function in 's' domain and divide the function in 't' time domain by t.

Answer : 2 (1-cos(at))/t

Answer 1

is this correct ?
\(\Large L^{-1}[\dfrac{d}{ds}F(s)] = (-1)^n\dfrac{f(t)}{t}\)
??

Answer 2

i am getting that answer with the formula
\(\Large L^{-1}[\dfrac{d}{ds}F(s)] = -tf(t)\)

wanted to confirm whether its correct or not...

Answer 3

Also, can someone verify whether this general formula is correct ot not...

\(\Large L^{-1}[\dfrac{d^n}{ds^n}F(s)] = (-1)^n t^nf(t)\)

Answer 4

Laplace transform of \[t ^{n}f(t)\]
\[L[t ^{n}f(t)]=(-1)^{n}. \frac{ d ^{n} }{ ds ^{n} }[F(s)]\]

Answer 5

yes, i used that to make that inverse laplace formula i posted...just wanted to be sure its absolutely correct...

Answer 6

so
\[L ^{-1}[(-1)^{n}\frac{ d ^{n} }{ ds ^{n}}[F(s)]]=t ^{n}f(t)\]

Answer 7

any references for such inverse lappy formulas ??

Answer 8

N.P. Bali (Engineering mathematics)

Answer 9

is it available online ? ebook ?

Answer 10

no..,you have to purchase it, it's available for purchasing online

Answer 11

or the most easy way ,search for laplace transform on google

Answer 12

i did...
but this is inverse laplace.....wiki didn't gave inverse laplace formulas...

Answer 13

*give

Answer 14

just you have to ajust all laplace transform formulas as i did to make them inverse laplace transform formulas .

Answer 15

yes, i did the same.
Thanks neer :)

Answer 16

you are welcome