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    Solution to the steady state load-deflection equation.

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    The steady state deflection is given by:

    y''''+c^4*y=f(x)

    calculate and plot the deflection for a load:

    f = 1 for |x|<10, f=0 everywhere else.

    using Fourier transform.

    Plot the deflection for various values of c.

    © BrainMass Inc. brainmass.com November 30, 2021, 12:10 am ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/solution-steady-state-load-deflection-equation-25360

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    Solution Preview

    Please see the attached file.

    The equation is:

    The Fourier transform of the equation is:

    The function is a simple "boxcar" function.

    A boxcar function of the form

    And:

    Thus:

    We need to evaluate:

    The integrand has 5 simple poles.
    One is obviously k=0 and the others are the roots of the equation:

    The roots ...

    Solution Summary

    the solution utilizes Fourier transform and complex-variables integration to solve this fourth order non-homogeneous differential equation. The solution contains 9 pages of derivations and graphs.

    $2.49

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