Finding the Inverse Laplace Transform of a Rational Function

[devillenator]

Homework Statement

hi guys, i need to find the inverse Laplace transform of

s/((s+1)^(2) +4)

the acual question is an IVP, i have worked trough it and am just about finished but i am stuck on this transform.

how would you go about getting this into a form that can be transformed like
2/((s+1)^(2) + 4)

or is it already and i am missing something

Homework Equations

i guess it can be changed to

s/(s^2 + 2s + 5) but that seems worse

The Attempt at a Solution

thanks for any help
i hope this is the right spot for this post

 

[lanedance]

hey devillinator - do you have to derive it yourself?

have a look at this list of standard Laplace transforms at http://www.vibrationdata.com/Laplace.htm and example 2.27 seems pretty useable

 

[devillenator]

thanks lanedance

i don't believe that i am expected to derive it myself as I am sure i read somewhere that i wasnt expected to for this course.

i have looked through a few simular tables without much luck I am afraid.



it may be possible that i messed up further up the question and have arived at a step i don't need to do, ill go back through and check things. hopefully i get lucky

 

[lanedance]

the form in the table matches your function though

 

[devillenator]

you mean 1/s^n, example 2.7a

i don't really see how that matches
s/((s+1)^(2) +4)

would it be possible for you to explain

 

[lanedance]

have a look at entry 2.27a as mentioned
$$\frac{s+\lambda}{(s+\alpha)^2 + \beta^2} \rightarrow e^{- \alpha t}(cos(\beta) \frac{\lambda - \alpha}{\beta}sin(\beta t))$$

 

[devillenator]

oh, cool, thanks.

missed that completely.


thanks again