Finding the Inverse Laplace Transform of a Rational Function

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Homework Help Overview

The discussion revolves around finding the inverse Laplace transform of the function s/((s+1)^(2) + 4) within the context of an initial value problem (IVP). Participants are exploring how to manipulate the function into a more recognizable form for transformation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to rewrite the function to match known forms for easier transformation. Some participants suggest checking standard Laplace transform tables for applicable forms, while others express uncertainty about the necessity of deriving the transform themselves.

Discussion Status

The discussion is active, with participants providing references to standard transform tables and clarifying specific entries that may be relevant to the original poster's problem. There is an acknowledgment of potential confusion regarding the steps taken in the problem, and some participants are revisiting their earlier work for accuracy.

Contextual Notes

Participants mention the possibility of having made errors earlier in the problem, which could affect the current step. There is also a reference to course expectations regarding derivation of transforms, indicating that not all participants may be required to derive them independently.

devillenator
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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
 
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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
 
the form in the table matches your function though
 
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
 
have a look at entry 2.27a as mentioned
[tex]\frac{s+\lambda}{(s+\alpha)^2 + \beta^2} \rightarrow e^{- \alpha t}(cos(\beta) \frac{\lambda - \alpha}{\beta}sin(\beta t))[/tex]
 
Last edited:
oh, cool, thanks.

missed that completely.


thanks again
 

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