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Math Help - Laplace Transformation Question 2

  1. #1
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    Laplace Transformation Question 2

    Here is the question:

    Given that:

    L{Cos(9t)/sqrt(pi*t)} = e^(-9/s)/sqrt(s)


    Find the laplace transformation of sqrt(t/pi)*Cos(9t)

    L{sqrt(t/pi)*Cos(9t)} = ?

    First I multiply the question by t/sqrt(t^2) which = 1

    and question becomes

    L(t * Cos(9t)/sqrt(pi*t))

    so by the theorem of Differentiation of Transforms

    my answer comes out to be

    (-1)^1 F'(s)

    = e^(-9/s)/(2e^(3/2)) - (9e^(-9/s)/s^(5/2))

    But it's wrong... please tell me what I did wrong!!

    Thank You!!
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  2. #2
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    Quote Originally Posted by Phyxius117 View Post
    Here is the question:

    Given that:

    L{Cos(9t)/sqrt(pi*t)} = e^(-9/s)/sqrt(s)


    Find the laplace transformation of sqrt(t/pi)*Cos(9t)

    L{sqrt(t/pi)*Cos(9t)} = ?

    First I multiply the question by t/sqrt(t^2) which = 1

    and question becomes

    L(t * Cos(9t)/sqrt(pi*t))

    so by the theorem of Differentiation of Transforms

    my answer comes out to be

    (-1)^1 F'(s)

    = e^(-9/s)/(2e^(3/2)) - (9e^(-9/s)/s^(5/2))

    But it's wrong... please tell me what I did wrong!!

    Thank You!!
    L[t \cdot f(t)] = - \frac{dF}{ds} where L[f(t)] = F(s). To get the derivative and check the steps, use this website: http://www.wolframalpha.com/
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