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Homework Help: Neeed help with a laplace transform

  1. Oct 17, 2005 #1
    What is the laplace transform of

    http://img150.imageshack.us/img150/8145/laplacetransform6wk.jpg [Broken]
     
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Oct 17, 2005 #2

    Tom Mattson

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    According to the section entitled "Homework Help" in the Physics Forums Global Guidelines which you agreed to:

    So whatcha got?
     
  4. Oct 17, 2005 #3
    It isn't so much to test, jsut to watch a tabel of formula, i know the transform for cos(x), but i can't find any rule which would let me multiplicat it with O(x).

    I mean for problems like this you jsut think, and try to figure out how to do it.
    I would say my problem is O(x).

    Anyway i got to go to bed now 00:08.. lol...
     
  5. Oct 17, 2005 #4

    Tom Mattson

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    Do you know what [itex]\theta(t)[/itex] is?
     
  6. Oct 18, 2005 #5

    for [itex]\theta(t)[/itex] t<0 gives t=0 and t>0 gives t=1 and the transform is 1/s, but that knowledge don't help me much :( ...
     
  7. Oct 18, 2005 #6

    Tom Mattson

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    You are right about [itex]\theta(t)[/itex], but that knowledge should help you a great deal.

    You have a function that is defined piecewise:

    [tex]\theta(t) = \left\{ \begin{array}{cc}0 & t<0\\1 & t \geq 0\end{array}[/tex]

    Now, if you multiply [itex]\theta(t)[/itex] by [itex]\cos(t)[/itex], then you just have to multiply both pieces by [itex]\cos(t)[/itex].

    So...

    [tex]\cos(t)\theta(t) = \left\{ \begin{array}{cc}0 & t<0\\\cos(t) & t \geq 0\end{array}[/tex]

    Can you take it from there?
     
    Last edited: Oct 18, 2005
  8. Oct 19, 2005 #7
    You missed that [itex]\theta(o)[/itex]=1/2 my text book say so, but it don't matter.

    Can I ignore [itex]\theta(t)[/itex] seen the laplace transform isn't defined for the second quadrant for the x-axis.

    Also i must ask how do you get access to all the special signs?

    Thx for your time Lorenz
     
  9. Oct 19, 2005 #8

    Galileo

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    It's not a matter of being undefined, but you got the right idea. It's more precise to state that the laplace transform of f doesn't care what values f takes on for x<0.

    What special signs?
     
  10. Oct 19, 2005 #9
    Like [itex]\theta(t)[/itex] i just copyed him there :smile:
     
  11. Oct 20, 2005 #10

    Galileo

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