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Math Help - laplace transforms are causing me trouble

  1. #1
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    laplace transforms are causing me trouble

    I'm having a little trouble with these laplace transforms, don't know why... they look pretty simple from first glance was wondering if someone could give me some direction solving these.

    1. exp(-at+b)

    2. sin(wt+b)

    3. cosh^23t
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  2. #2
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    Quote Originally Posted by action259
    exp(-at+b)
    I assume a>0.
    ---
    e^{-at+b}
    Now there is no rule for that. But you need to change it.
    You can write.
    e^{-at}e^b because the product of these is adding exponents.

    Remember that,
    \mathcal{L}e^{-at}=\frac{1}{s+a}
    And,
    \mathcal{L}\{\kappa f(x)\}=\kappa \mathcal{L}\{f(x)\}

    Since, e^b is a KoNsTaNt.
    We have,
    \frac{e^b}{s+a}
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  3. #3
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    Quote Originally Posted by action259
    sin(wt+b)
    Did you Botox it?
    \sin \omega t\cos b+\cos \omega t\sin b
    And, b is a KoNsTaNt.
    Apply the rules,
    \mathcal{L}\{ \sin at\}=\frac{a}{s^2+a^2}
    \mathcal{L}\{ \cos at\}=\frac{s}{s^2+a^2}
    Thus,
    \frac{\omega \cos b}{s^2+\omega^2}+\frac{s\sin b}{s^2+\omega^2}
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  4. #4
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    Quote Originally Posted by action259
    cosh^23t
    The problem is that you have a square. However, you can eliminate it.
    Use the following identity,
    \cosh^2 x=\frac{1+\cosh 2x}{2}
    This will eliminate the square and turn it into one of the forms on the table.
    (If you want I can prove that identity. The reason why I am saying this is because my Calculus book does not contain this identity on its treatise on hyperbolic functions. Thus, I assumed might be unfamiliar).
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