Finding the Inverse Laplace Transformation

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Homework Help Overview

The discussion revolves around finding the inverse Laplace transformation of the expression \(\frac{5s+4}{s^2} e^{-2s}\). Participants are exploring the implications of the second shifting theorem and the transformation process itself.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the use of partial fractions for the expression \(\frac{5s+4}{s^2}\) and the necessity of incorporating the unit step function \(u(t-2)\) due to the shifting factor \(e^{-2s}\). There are questions about the correctness of derived answers and the steps needed to reach the expected result.

Discussion Status

Some participants are confirming their interpretations of the inverse Laplace transformation process, while others are questioning the correctness of their results. There is acknowledgment of the need to clarify the transformation of the initial expression before applying the shifting theorem.

Contextual Notes

Participants are working under the constraints of homework guidelines, which may limit the information they can share or the methods they can use. There is a focus on ensuring that the assumptions regarding the transformation and the shifting theorem are correctly understood.

izen
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Homework Statement



find the inverse laplace transformation of [itex]\frac{5s+4}{s^2}[/itex] e[itex]^{-2s}[/itex]

Homework Equations

The Attempt at a Solution



I have tried to partial fractions [itex]\frac{5s+4}{s^2}[/itex] and I got [itex]\frac{5}{s}[/itex]+[itex]\frac{4}{s^2}[/itex] and I know that the answer must have u(t-2) because of second shifting ( a=2)

but I looked at the answer from this question is 5 u(t-2)(e[itex]^{4(t-2)}[/itex] - e[itex]^{-(t-2)}[/itex]).

I don't know how to get that answer please help
 
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The answer is wrong.
 
so my answer is [5+4(t-2)] u(t-2) Is my answer right?
thank you
 
izen said:

Homework Statement



find the inverse laplace transformation of [itex]\frac{5s+4}{s^2}[/itex] e[itex]^{-2s}[/itex]

Homework Equations




The Attempt at a Solution



I have tried to partial fractions [itex]\frac{5s+4}{s^2}[/itex] and I got [itex]\frac{5}{s}[/itex]+[itex]\frac{4}{s^2}[/itex] and I know that the answer must have u(t-2) because of second shifting ( a=2)

but I looked at the answer from this question is 5 u(t-2)(e[itex]^{4(t-2)}[/itex] - e[itex]^{-(t-2)}[/itex]).

I don't know how to get that answer please help

First: what is the inverse Laplace transform of ##(5s+4)/s^2##? Next: worry about the effect of the factor ##e^{-2s}##.
 
izen said:
so my answer is [5+4(t-2)] u(t-2) Is my answer right?
thank you
Yes, that's correct.
 
Thanks you all
 

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