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Math Help - Solving a Mass-spring-damped system with Laplace

  1. #1
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    Solving a Mass-spring-damped system with Laplace

    the equation is given, x'' + 4x' + 4x = f(t)

    where f(t) = { t , 0 < t < 2 ; 0 , 2 < t }

    I am having trouble getting the laplace of the f(t) function.

    I believe you would get L{f(t)} == L { [1 - H(t-2)]t }

    Which would be L{t} - L{ t*H( t-2 ) }

    Which I think would be 1/u^2 - (e^-2u)/u^2

    Which Is  (1-e^-2u)/u^2, but this is incorrect.

    The solution is 1/u^2 - (e^-2u)[2/s +1/u^2]

    is there anyone that could help me? Thank you in advance
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  2. #2
    MHF Contributor chisigma's Avatar
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    Why You simply don't compute the integral...

    \mathcal{L}\{f(t)\} = \int_{0}^{2} t\cdot e^{-ut}\cdot dt (1)

    ... ?...

    Kind regards

    \chi \sigma
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