How Do You Transform and Simplify the Inverse Laplace Function 1/[s(2s^2+2s+1)]?

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SUMMARY

The discussion focuses on transforming the function 1/[s(2s^2+2s+1)] to facilitate finding its inverse Laplace transform. The user successfully modified the function to 0.5/[s(s+0.5)^2 + 0.5^2](1/0.5) but struggles with the algebraic manipulation required to simplify it further. A suggested transformation involves expressing the function as (1/s) - [(s+0.5)+0.5]/[(s+0.5)^2+0.5^2], which simplifies the process of obtaining the inverse Laplace transform. The user seeks clarification on the properties and steps necessary for this transformation.

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fern518
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Hey everyone.

I've got through most of a problem that involves finding an inverse laplace transform, but I am stuck at one part that requires algebraic manipulation. The function is

1/[s(2s2+2s+1)]

So far I have modified it too look like .5/[s(s+.5)2 +.52](1/.5)

I'm not sure how to modify the function with that extra s in the denominator.

I had seen that the function could be transformed into (1/s) - [(s+.5)+.5]/[(s+.5)2+.52 and then from that the inverse Laplace could be easily obtained, but I am not sure how this transformation was done. I am sure there is a property I'm not thinking of, but any help on this would be greatly appreciated!
 
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You can consider like this
[tex] \frac{1}{s(s+a)^2}=\frac{A}{s}+\frac{Bs+C}{(s+a)^2}[/tex]
From the above equation find A, B and C values by substituting different values of s.
 

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