My Math Forum Laplace transform

 Differential Equations Ordinary and Partial Differential Equations Math Forum

July 1st, 2017, 05:26 PM   #1
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Laplace transform

I don't know how the transform was determined from the solution that the book gave.
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 July 1st, 2017, 07:25 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,320 Thanks: 450 Math Focus: Yet to find out. There may be a quicker way with some tricky substitution or something, but i haven't looked at it for very long. But you can just work through the algebra for this. You will end up with a bunch of similar terms which will likely factor out and result in the above equation. Nothing new here that i can see.
 July 3rd, 2017, 08:18 PM #3 Senior Member     Joined: Jul 2012 From: DFW Area Posts: 603 Thanks: 83 Math Focus: Electrical Engineering Applications Hi bdewbac, I worked the problem using the delay ($t$ shift) property of the Laplace Transform: $\displaystyle \large f(t-t_0) \ u(t-t_0) \Leftrightarrow e^{-st_0}F(s)$ Since: $\displaystyle \large t \ u(t) \Leftrightarrow \frac{1}{s^2}$ Then, for example: $\displaystyle \large 10 \ (t-2) \ u(t-2) \Leftrightarrow 10 \frac{e^{-2s}}{s^2}$ I hope that this helps.

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