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Math Help - Piecewise Laplace 1

  1. #1
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    Piecewise Laplace 1

    y'' + 81y = T(t)

    where T(t) =

    4t from 0 to 7
    28 from 7 to infinity

    y(0) = 0, y'(0) = 0

    Find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)

    I took Laplace of both side and answer comes out to be


    (1/(1-e^(-7s)))((4(1-e^(-7s)(7s+1))/s^2+(28*e^(-7s)/s)))(1/(s^2+81))

    but it's wrong.. please help!!
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  2. #2
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    Quote Originally Posted by Phyxius117 View Post
    y'' + 81y = T(t)

    where T(t) =

    4t from 0 to 7
    28 from 7 to infinity

    y(0) = 0, y'(0) = 0

    Find the equation you get by taking the Laplace transform of the differential equation and solve for Y(s)

    I took Laplace of both side and answer comes out to be


    (1/(1-e^(-7s)))((4(1-e^(-7s)(7s+1))/s^2+(28*e^(-7s)/s)))(1/(s^2+81))

    but it's wrong.. please help!!
    T(t) = 4t [H(t) - H(t - 7)] + H(t - 7) = 4t H(t) - (4t - 1) H(t - 7) where H(t) is the Heaviside Step Function: Heaviside step function - Wikipedia, the free encyclopedia
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  3. #3
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    but my professor never taught us how to take Laplace of Heaviside functions...this is so frustrating lol
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  4. #4
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    Thanks! I figured this one out. the answer is


    (4(1-e^(-7s)(7s+1))/s^2+(28*e^(-7s)/s))(1/(s^2+81))
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