Understanding the Inverse Laplace Transform: Solving for 3/s√(π)

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Homework Help Overview

The discussion revolves around the inverse Laplace transform of the expression 3/s√(π). Participants are exploring the steps involved in finding the inverse transform and the reasoning behind certain manipulations of the expression.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the transformation steps taken, questioning the rationale behind multiplying by √(π) and the specific Laplace transform used to derive the result from L-1{√(π)/√(s)} to 1/√(t). There is also inquiry into the value of n in the context of the problem.

Discussion Status

The discussion is active, with participants seeking clarification on specific steps and transformations. Some guidance has been offered regarding the identification of relevant Laplace transforms, but there is no explicit consensus on the interpretations or methods being discussed.

Contextual Notes

Participants reference a Laplace transform table for assistance and express uncertainty about the correct transform to use, indicating potential gaps in information or understanding of the material.

jdawg
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Homework Statement


L-1{3/s1/2}

Homework Equations

The Attempt at a Solution


3L-1{1/s1/2}

3L-1{(1/sqrt(π))(sqrt(π)/(sqrt(s))}

3/(sqrt(π))L-1{(sqrt(π))/(sqrt(s))}

3/(sqrt(π))(1/(sqrt(t))

This is what I got from the solution for this problem. What tipped them off to multiply by sqrt(π)? And which Laplace transform did they use to go from L-1{sqrt(π)/sqrt(s)} to 1/sqrt(t)? I can't seem to find the right one on my table.Thanks!
 
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jdawg said:

Homework Statement


L-1{3/s1/2}

Homework Equations

The Attempt at a Solution


3L-1{1/s1/2}

3L-1{(1/sqrt(π))(sqrt(π)/(sqrt(s))}

3/(sqrt(π))L-1{(sqrt(π))/(sqrt(s))}

3/(sqrt(π))(1/(sqrt(t))

This is what I got from the solution for this problem. What tipped them off to multiply by sqrt(π)? And which Laplace transform did they use to go from L-1{sqrt(π)/sqrt(s)} to 1/sqrt(t)? I can't seem to find the right one on my table.Thanks!
See http://tutorial.math.lamar.edu/classes/de/laplace_table.aspx. #6 looks like it would work here.
 
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Ok! So what is n in this case? Does n=0?
 
jdawg said:
Ok! So what is n in this case? Does n=0?
Yes
 
Thanks!
 

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