Ugh I hate Laplace Transforms

  • NerdLifter

    Posts: 1509

    Apr 25, 2011 7:14 PM GMT
    Anyone know the Laplace transform for:

    Laplace1.png


    icon_question.gif


    Need it to solve for a signal's energy density. I simplified the equation before posting it; don't worry I know what the t and omega naughts are.
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    Apr 25, 2011 7:15 PM GMT
    It looks like a very complicated way of saying LOLWUT.
  • NerdLifter

    Posts: 1509

    Apr 25, 2011 7:23 PM GMT
    I tried to break it down and do the transform manually, but there are so many places one could screw up, which is why getting it from a table is preferred but I haven't found one.

    Here is the transform I attempted:

    Laplace2.png
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    Apr 25, 2011 7:24 PM GMT
    I think I'm glad I was a liberal arts major.
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    Apr 25, 2011 7:29 PM GMT
    LOL. I got through stats 3 and Operations Analysis by being clever. I am great at math but too lazy to do it on paper. And this is why I am sticking to Managing Information Systems and Programming. I just program stuff like this into my calculator or was able to solve it by programming in excel.

    icon_lol.gif
  • NerdLifter

    Posts: 1509

    Apr 25, 2011 7:34 PM GMT
    I get the strong feeling that the following Laplace transform found in the back of the book is connected and that we have to somehow manipulate it:

    Laplace3.png


    Ideas icon_idea.gif ?
  • NerdLifter

    Posts: 1509

    Apr 26, 2011 5:55 PM GMT
    Alas, had to turn it in without knowing the correct transform pair.
  • iHavok

    Posts: 1477

    Apr 26, 2011 6:01 PM GMT
    Studinprogress saidAnyone know the Laplace transform for:

    Laplace1.png


    icon_question.gif


    Need it to solve for a signal's energy density. I simplified the equation before posting it; don't worry I know what the t and omega naughts are.


    A) Bit too far out of school to be of assistance.

    B) Slightly turned on by this thread. LOL


    Hot Gay Nerd. Yum!
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    Apr 26, 2011 6:06 PM GMT
    Just wait until you have to apply Laplace Transforms and Taylor Expansions to physical chemistry! UGH I hated my major! I can't remember how to do that at all, but have you tried http://www.wolframalpha.com/? This thing is amazing if you take the 5-10 minutes to learn how to use it.
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    Apr 26, 2011 6:18 PM GMT
    holy crap i havent seen that in years. brings back horrible memories of engineering classes! good luck man

    iHavok said

    A) Bit too far out of school to be of assistance.

    B) Slightly turned on by this thread. LOL



    and ps... i was thinking the same thing!
  • joarky123

    Posts: 264

    Apr 26, 2011 6:20 PM GMT
    working systems engineer. the laplace transform is my bitch! too bad i never saw this in time. sorry stud
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    Apr 26, 2011 6:27 PM GMT
    Studinprogress saidAnyone know the Laplace transform for:

    Laplace1.png


    icon_question.gif


    Need it to solve for a signal's energy density. I simplified the equation before posting it; don't worry I know what the t and omega naughts are.


    http://www.youtube.com/watch?v=uXO2hsv2SlE
  • ursa_minor

    Posts: 566

    Apr 26, 2011 6:50 PM GMT
    i already forgot my Laplace, but i would make use of 1) the cosine - sine squared identities or the 2) the differential relationship of those 2 functions (you know, d(cos) = -sine, or d(sin) = cos) and then proceed with Laplace of the differentials
  • mmmm_mmmm

    Posts: 1658

    Apr 26, 2011 7:11 PM GMT
    IF I had the time I would work it out for you.
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    Apr 26, 2011 7:16 PM GMT
    they actually use it in real life?

    I gave it all back to my professor after I graduated...
  • NerdLifter

    Posts: 1509

    Apr 26, 2011 7:20 PM GMT
    hazardous saidJust wait until you have to apply Laplace Transforms and Taylor Expansions to physical chemistry! UGH I hated my major! I can't remember how to do that at all, but have you tried http://www.wolframalpha.com/? This thing is amazing if you take the 5-10 minutes to learn how to use it.


    We have been doing Taylor Expansions and Laplace transforms since sophomore year.

    I know all about wolframalpha and use it often to do calculations; however, unfortunately, it cannot compute special Laplace transformation cases icon_sad.gif only simple ones.
  • NerdLifter

    Posts: 1509

    Apr 26, 2011 7:21 PM GMT
    SFYogi said
    Studinprogress saidAnyone know the Laplace transform for:

    Laplace1.png


    icon_question.gif


    Need it to solve for a signal's energy density. I simplified the equation before posting it; don't worry I know what the t and omega naughts are.


    http://www.youtube.com/watch?v=uXO2hsv2SlE


    icon_biggrin.gif Perfect family guy clip.
  • NerdLifter

    Posts: 1509

    Apr 26, 2011 7:24 PM GMT
    blue_ahli saidi already forgot my Laplace, but i would make use of 1) the cosine - sine squared identities or the 2) the differential relationship of those 2 functions (you know, d(cos) = -sine, or d(sin) = cos) and then proceed with Laplace of the differentials


    If you do that, it'll look nothing like any of the Laplace pairs provided, making it even more useless icon_sad.gif

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    Apr 26, 2011 7:59 PM GMT
    Based on the first equation you gave, I distributed and just took the Laplace of each, which gives you:

    (e^(-s))/s - s/((s^2) + (w_0)^2) - (e^(-(t_0)s))/s - L(cos(w_0)t*u(t-t_0))

    For the last part its just a delayed step which you could get the transform for cosine and then multiply it with the exponential of the delay, but I'm not completely sure, so I would use convolution to get the right answer for sure.

    Hope this helps a little.
  • UVaRob9

    Posts: 282

    Apr 26, 2011 8:12 PM GMT
    Laplace(u(t)) - Laplace(u(t-t0) - Laplace(cos(w0*t)*u(t) + Laplace(cos(w0*t)*u(t-t0)) was what I found. I tried Maple and it doesn't seem to have a concise form, so I think you really do have to distribute it out since your functions are assumed to be linear and {a f(t) + b g(t)} = a{f(t)} + b{g(t)}.
  • NerdLifter

    Posts: 1509

    Apr 26, 2011 8:13 PM GMT
    rsod44 saidBased on the first equation you gave, I distributed and just took the Laplace of each, which gives you:

    (e^(-s))/s - s/((s^2) + (w_0)^2) - (e^(-(t_0)s))/s - L(cos(w_0)t*u(t-t_0))

    For the last part its just a delayed step which you could get the transform for cosine and then multiply it with the exponential of the delay, but I'm not completely sure, so I would use convolution to get the right answer for sure.

    Hope this helps a little.


    When I look back at the homework, I'll let ya know ;)
  • NerdLifter

    Posts: 1509

    Apr 26, 2011 8:15 PM GMT
    UVaRob9 saidLaplace(u(t)) - Laplace(u(t-t0) - Laplace(cos(w0*t)*u(t) + Laplace(cos(w0*t)*u(t-t0)) was what I found. I tried Maple and it doesn't seem to have a concise form, so I think you really do have to distribute it out since your functions are assumed to be linear and {a f(t) + b g(t)} = a{f(t)} + b{g(t)}.


    As the later steps show, I already distributed it out. That is elementary Laplace rules 101 icon_wink.gif
  • UVaRob9

    Posts: 282

    Apr 26, 2011 8:21 PM GMT
    Um, okay. I thought what you originally posted *was* the factored expression you were trying to transform. Wouldn't you just use convolution anyway?
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    Apr 26, 2011 8:29 PM GMT
    Sorry, no need for nasty convolution. Just verified some stuff and the Laplace of the last part should be just their multiplication:

    (se^-(t_0)s)/(s^2 + (w_0)^2)
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    Apr 27, 2011 2:33 AM GMT
    Go back to basics and use the definition of the Laplace transform. The difference of the two step functions means you're just doing a definite integral from t=0 to t=t_0. This can be handled by Wolfram Alpha. Writing a instead of w_0, and writing b instead of t_0, your request would be:

    integrate (1-cos(a*t)) * exp(-s*t) from t=0 to b