Question

I need help in finding inverse Laplace transformation of e^(-5s)/(2s^2+s+2)

Answer 1

still need help ?

Answer 2

yes

Answer 3

do you know the identity
\(\huge L^{-1}[e^{-as}F(s)]=f(t-a)u(t-a)\)
?

Answer 4

yes

Answer 5

so, you first need laplace inverse of 1/(2s^2+s+2)
right ?

Answer 6

yes, I think I have it.

Answer 7

ohh...so you were able to find laplace inverse of 1/(2s^2+s+2) ??

Answer 8

yes. It's this
\[\frac{ 2 }{ \sqrt{15} }e ^{-t/4}\sin(\frac{ \sqrt{15} }{ 4 }t)\]

Answer 9

I hope :D

Answer 10

\[\checkmark\]

Answer 11

and this is where I don't know what to do next

Answer 12

yes, thats correct, now just replace, t by 't-5'
and add u(t-5) in the end.
using that formula....

Answer 13

\(\huge \frac{ 2 }{ \sqrt{15} }e ^{(-t+5)/4}\sin(\frac{ \sqrt{15} }{ 4 }(t-5))u(t-5)\)

Answer 14

thank you :)

Answer 15

welcome ^_^