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Math Help - laplace tranforms of sin and cos???

  1. #1
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    laplace tranforms of sin and cos???

    f(t)=3sin(t)+5cos(3t)

    i am not familiar with laplace of sin and cos functions
    anyone help?
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  2. #2
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    Table of Laplace Transforms

    Particularly,

    \mathcal{L}(\cos(ax)) = \frac{s}{s^2 + a^2}
    \mathcal{L}(\sin(ax)) = \frac{a}{s^2 + a^2}
    \mathcal{L}(c*f(t)) = c*\mathcal{L}(f(t)) \, \text{for any} \, c \in \mathbb{R}
    Last edited by mr fantastic; December 2nd 2009 at 11:27 AM. Reason: Put latex text in textbox
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  3. #3
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    Ive just tried to answer the question ...I would like to know if the answer i found is right..
    Qn: laplace of (f(t)=3sin(t)+5cos(3t))

    L{f(t)}=3L{sin(t)}+5L{cos(3t)}

    =3(1/(s^2+1))+5(s/(s^2+9))
    On further simplification
    =5s^3+3s^2+5s+27/(s^2+1)(s^2+9)
    Last edited by mr fantastic; January 15th 2010 at 04:06 PM. Reason: Fixed defect.
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