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Math Help - [SOLVED] inverse Laplace transforms

  1. #1
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    Red face [SOLVED] inverse Laplace transforms

    Hi all.

    I am doing some study for exams and have become completely stuck on Laplace transforms, mainly inverse Laplace transforms.

    These are the three that I am having trouble with:

    a) 1/(s^2 -2s-15)


    b) e^-2s / (s+4)


    c) 1/(s^2 +9)


    any help would be great

    thanks
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  2. #2
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    Quote Originally Posted by hellhound View Post
    Hi all.

    I am doing some study for exams and have become completely stuck on Laplace transforms, mainly inverse Laplace transforms.

    These are the three that I am having trouble with:

    a) 1/(s^2 -2s-15)


    b) e^-2s / (s+4)


    c) 1/(s^2 +9)


    any help would be great

    thanks
    a) Factorise the denominator, perform a partial fraction decomposition and use tables to recognise standard forms.

    b) You're expected to know the 'second shift theorem': LT[f(t)] = F(s) then LT[u(t - a) f(t - a)] = e^{-as} F(s). In your case F(s) is a standard form.

    c) You have  \frac{1}{3} \, \frac{3}{s^2 + 3^2}. Use tables to recognise a standard form.
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  3. #3
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    wow thank you. I dont know why I didn't see those before, I've done heaps of these. Anyway thank you again.
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