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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
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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.
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July 3rd, 2017, 08:18 PM   #3
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Hi bdewbac,

I worked the problem using the delay ($t$ shift) property of the Laplace Transform:

$\displaystyle \large f(t-t_0) \ u(t-t_0) \Leftrightarrow e^{-st_0}F(s)$


$\displaystyle \large t \ u(t) \Leftrightarrow \frac{1}{s^2}$

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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