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Inverse Laplace Transformation of arctan (s/2) 
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#1
Nov912, 05:11 PM

P: 3

The Title pretty much says it all. I'm trying to learn how to solve the Inverse Laplace Transformation of Arctan(s/2). An equation of this sort was not explicitly covered in class and I'm having difficulty figuring where to start to solve it. If anyone could give me a general idea that would point me in the right direction that would be greatly appreciated.
Thanks in advance 


#2
Nov912, 08:26 PM

P: 3

The derivative of arctan(t)=1/(t^2+1). Differentiation in timedomain is the same as multiplication by s in Laplacedomain. See http://en.wikipedia.org/wiki/Laplace_transform for a table. You should be able to derive the correct answer from this.



#3
Nov1012, 02:25 PM

P: 3

Thank you! This helped, although I'm still not sure what exactly is meant by "Differentiation in timedomain is the same as multiplication by s in Laplacedomain. " But like I said this got my started on the way to solve the problem.



#4
Nov1812, 03:59 AM

P: 761

Inverse Laplace Transformation of arctan (s/2)
Hi nileszoso!
A classical method to compute the inverse Laplace transform is the use of the Bromwich integral. In the case of arctan(s/2) this leads to ardous calculus with special functions. Moreover, the inverse Laplace Transform of arctan(s) doesn't appears in some extended tables. So, it is questionable whether there is really a solution which can be expressed with not too complicated combinations of standard functions. Where this problem is coming from ? 


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