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Math Help - Laplase Transformations! PLEASE HELP!!

  1. #1
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    Laplase Transformations! PLEASE HELP!!

    Find the Laplace transformation:
    I think a convolution is necessary, Please Help!
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  2. #2
    Lord of certain Rings
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    Quote Originally Posted by Bananna View Post
    Find the Laplace transformation:
    I think a convolution is necessary, Please Help!
    Nice question

    By sifting property,

    \cos(t) \delta(t-3\pi)  = \cos(3\pi) \delta(t-3\pi)

    Now do you know the Laplace Transform of a shifted impulse?
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    and


    But I dont know how they go together
    Please help
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  4. #4
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    NO!
    \cos(3\pi) = -1, it is a constant...
    --------------------------------------------------------------------
    Quote Originally Posted by Bananna View Post
    and


    But I dont know how they go together
    Please help
    If c is a constant and L(\delta(t-3\pi)) = e^{-3\pi s}

    Then what is L(c\delta(t-3\pi)) \text{ ?}
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  5. #5
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    duh....I have been staring at these problems.
    L(1)=1/s
    so the L(-1) must be -1/s
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  6. #6
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    Quote Originally Posted by Bananna View Post
    duh....I have been staring at these problems.
    L(1)=1/s
    so the L(-1) must be -1/s
    Right.. so what is
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  7. #7
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    Quote Originally Posted by Isomorphism View Post

    NO!
    \cos(3\pi) = -1, it is a constant...
    --------------------------------------------------------------------


    If c is a constant and L(\delta(t-3\pi)) = e^{-3\pi s}

    Then what is L(c\delta(t-3\pi)) \text{ ?}


    is that it?
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  8. #8
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    Quote Originally Posted by Isomorphism View Post
    Right.. so what is


    ...???
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  9. #9
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    Quote Originally Posted by Bananna View Post
    Find the Laplace transformation:
    I think a convolution is necessary, Please Help!
    Are you trying to get the Laplace transform of the product? If so, just use the definition:

    LT[\cos (t) \delta(t - 3 \pi)] = \int_{0}^{\infty} e^{-st} \, \cos (t) \delta(t - 3 \pi) \, dt

    and use the sifting property of the Dirac delta function.
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