Laplace Transformation: Transforming F(s) = 1/(s-2)^2

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Homework Help Overview

The discussion revolves around the Laplace transformation of the function F(s) = 1/(s-2)^2, focusing on identifying the appropriate transformation techniques and rules from a reference table.

Discussion Character

  • Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants explore different entries in a transformation table to find a suitable match for the given function. There is discussion about the relevance of the "frequency shifting rule" and its application to the transformation process.

Discussion Status

Some participants have offered guidance on which entries in the transformation table may apply, while others have pointed out potential misunderstandings regarding the counting of entries. Multiple interpretations of the relevant rules are being explored.

Contextual Notes

There appears to be some confusion regarding the specific entries in the transformation table and how they relate to the function being transformed. The discussion also hints at the use of specific rules that may not be explicitly stated in the original problem context.

leopard
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How can I transform

[tex]F(s) = \frac{1}{(s-2)^2}[/tex]

?

I cannot see that any of the functions in my table is useful...

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Use the third one in the list along with the "frequency shifting rule": [tex]\mathcal{L}^{-1}[F(s-\alpha)]=e^{\alpha t}\mathcal{L}^{-1}[F(s)][/tex]
 
Actually, it's the second one in the list: the Laplace transform of 1/t is 1/s2. I think gabbagabbahey was counting the heading. Also note that gabbagabbahey's "frequency shifting rule" is implied in the third, the Laplace transform of eat is 1/(s-a) which is just the laplace transform of 1/t "shifted" by a.
 
HallsofIvy said:
... I think gabbagabbahey was counting the heading...

Actually I meant the third (with n=1 of course)---but certainly the second is a little more straightforward!:smile:
 

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