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Math Help - Find the Laplace transform of each of the following:

  1. #1
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    Find the Laplace transform of each of the following:

    (a) e^4t
    (b) 4 e^2t + 3 cosh 4t
    (c) 2 sin3t + 4 sinh 3t
    (d) t^3 + 2t^2 - 4t + 1
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by tone999 View Post
    (a) e^4t
    (b) 4 e^2t + 3 cosh 4t
    (c) 2 sin3t + 4 sinh 3t
    (d) t^3 + 2t^2 - 4t + 1
    Just apply the formulas! Also note that the Laplace Transform is linear (I did two of them for you):

    (a) \mathcal{L}\left\{e^{4t}\right\}=\frac{1}{s-4}

    (c) \mathcal{L}\left\{2\sin\left(3t\right)+4\sinh\left  (3t\right)\right\}=2\mathcal{L}\left\{\sin\left(3t  \right)\right\}+4\mathcal{L}\left\{\sinh\left(3t\r  ight)\right\} =2\cdot\frac{3}{s^2+9}+4\cdot\frac{3}{s^2-9}=\frac{6s^2-54+12s^2+108}{s^4-81}=\frac{18\left(s^2+3\right)}{s^4-81}

    If you can't use the short cuts, then apply the definition:

    \mathcal{L}\left\{f\left(t\right)\right\}=\int_0^{  \infty}e^{-st}f\left(t\right)\,dt

    I hope this helps...
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