Homework Help: Inverse Laplace transform

1. Oct 16, 2009

devillenator

1. The problem statement, all variables and given/known data
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

2. Relevant equations

i guess it can be changed to

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

3. The attempt at a solution

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

2. Oct 16, 2009

lanedance

3. Oct 16, 2009

devillenator

thanks lanedance

i dont believe that i am expected to derive it myself as im sure i read somewhere that i wasnt expected to for this course.

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

it may be possible that i messed up further up the question and have arived at a step i dont need to do, ill go back through and check things. hopefully i get lucky

4. Oct 17, 2009

lanedance

the form in the table matches your function though

5. Oct 17, 2009

devillenator

you mean 1/s^n, example 2.7a

i dont really see how that matches
s/((s+1)^(2) +4)

would it be possible for you to explain

6. Oct 17, 2009

lanedance

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

Last edited: Oct 18, 2009
7. Oct 18, 2009

devillenator

oh, cool, thanks.

missed that completly.

thanks again