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

[jdawg]

Homework Statement

L^-1{3/s^1/2}

Homework Equations

The Attempt at a Solution

3L^-1{1/s^1/2}

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!

 

[Mark44]

Homework Statement

L^-1{3/s^1/2}

Homework Equations

The Attempt at a Solution

3L^-1{1/s^1/2}

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.

 

[jdawg]

Ok! So what is n in this case? Does n=0?

 

[Mark44]

Ok! So what is n in this case? Does n=0?

Yes

 

[jdawg]

Thanks!