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 March 4th, 2013, 08:23 AM #1 Newbie   Joined: Apr 2012 Posts: 8 Thanks: 0 Inverse Laplace of: (1) / ( (1+s)^2 +1 ) = ? Will you please tell which conversions from the table did you use, and how did you used them for solving it? THanks
 March 4th, 2013, 12:07 PM #2 Math Team     Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions Re: Inverse Laplace of: (1) / ( (1+s)^2 +1 ) = ? First notice that $\mathcal{L}(\sin(t))=\frac{1}{s^2+1}$ But we there we have (s+1) instead of s so : $\mathcal{L}(e^{-t}\sin(t))=\frac{1}{(s+1)^2+1}$
March 5th, 2013, 12:04 AM   #3
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Re: Inverse Laplace of: (1) / ( (1+s)^2 +1 ) = ?

Quote:
 Originally Posted by zaidalyafey First notice that $\mathcal{L}(\sin(t))=\frac{1}{s^2+1}$ But we there we have (s+1) instead of s so : $\mathcal{L}(e^{-t}\sin(t))=\frac{1}{(s+1)^2+1}$
Thanks for answering Ok now can I see a reference or documentation for this? I mean where you add +1 to s and it equals $e^{-t}$ ? Perhaps a web page or a book?

March 5th, 2013, 03:34 AM   #4
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Re: Inverse Laplace of: (1) / ( (1+s)^2 +1 ) = ?

Quote:
 Originally Posted by baylar10 Ok now can I see a reference or documentation for this? I mean where you add +1 to s and it equals $e^{-t}$ ? Perhaps a web page or a book?
you always can prove it yourself using :

$\mathcal{L}(f(t))=\int^{\infty}_0\,e^{-st}f(t)\,dt$

When I first learned about Laplace I looked at this PDF file, it is very helpful :

March 5th, 2013, 06:31 AM   #5
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Re: Inverse Laplace of: (1) / ( (1+s)^2 +1 ) = ?

Quote:
Originally Posted by zaidalyafey
Quote:
 Originally Posted by baylar10 Ok now can I see a reference or documentation for this? I mean where you add +1 to s and it equals $e^{-t}$ ? Perhaps a web page or a book?
you always can prove it yourself using :

$\mathcal{L}(f(t))=\int^{\infty}_0\,e^{-st}f(t)\,dt$

When I first learned about Laplace I looked at this PDF file, it is very helpful :
Thanks very much for the book Turns out you have to use First shifting rule!

 March 5th, 2013, 06:38 AM #6 Math Team     Joined: Aug 2012 From: Sana'a , Yemen Posts: 1,177 Thanks: 44 Math Focus: Theory of analytic functions Re: Inverse Laplace of: (1) / ( (1+s)^2 +1 ) = ? yep, excellent. Have you read it all ?
March 5th, 2013, 11:13 AM   #7
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Re: Inverse Laplace of: (1) / ( (1+s)^2 +1 ) = ?

Quote:
 Originally Posted by zaidalyafey yep, excellent. Have you read it all ?
No way!!!

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