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Math Help - Help with Laplace Transforms!

  1. #1
    Member zangestu888's Avatar
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    Help with Laplace Transforms!

    I hope am in the right topic section hear i have this question i need guidance with its a laplace transform still kind fuzy on this topic the question is

    find the laplace trasnform of u(t-2)(t^2+4t-5) i dont know what to do going over my notes and txt i think its a second shifting theorm question so L{u(t-a)f(t-a)}=e^-asF(s) but stilll am not sure about it being first or second or what the difference itself is, any help please and if anyoe can guide me to some more examples i need help with thiese thanks!
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  2. #2
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    Quote Originally Posted by zangestu888 View Post
    find the laplace trasnform of u(t-2)(t^2+4t-5) i dont know what to do going over my notes and txt i think its a second shifting theorm question so L{u(t-a)f(t-a)}=e^-asF(s) but stilll am not sure about it being first or second or what the difference itself is, any help please and if anyoe can guide me to some more examples i need help with thiese thanks!
    I think you need to be more clear... you have u's and t's in your function, and I'm not sure what is what. Is u(t) the unit step function, which is 0 for t<0 and 1 for t\geq 0?
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  3. #3
    Member zangestu888's Avatar
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    al am asked in my question is find the laplace transform of
    u(t-2)(t^2+4t-5) ? lol am sure its one of the shifting theorms but not sure how to apply it
    Last edited by mr fantastic; July 13th 2009 at 08:26 PM. Reason: Corrected spelling of shifting ....
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  4. #4
    Super Member Random Variable's Avatar
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    I'm assuming that it's already in the correct form, namely u(t-2)f(t-2) .

    So if  f(t-2) = t^{2}+4t-5, then  f(t)= (t+2)^{2}+4(t+2)-5 = t^{2}+8t +7

    and  F(s) = \mathcal{L} [t^{2}+8t+7] = \frac {2}{s^{3}} + \frac{8}{s^{2}} + \frac{7}{s}

     \mathcal{L} [u(t-2)f(t-2)] = e^{-2s}\Big( \frac {2}{s^{3}} + \frac{8}{s^{2}} + \frac{7}{s}\Big)
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  5. #5
    Member zangestu888's Avatar
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    where did the f(t-2) come from? is it becuase i have to have both u and f the same shift and it became t+2 becuase of the shift correct?
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  6. #6
    Super Member Random Variable's Avatar
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    Quote Originally Posted by zangestu888 View Post
    where did the f(t-2) come from? is it becuase i have to have both u and f the same shift and it became t+2 becuase of the shift correct?
    I'm assuming that what's given is u(t-2)f(t-2). But the theorem calls for the transform of f(t).
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