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Math Help - 2nd ordr homogenoues ODEs

  1. #1
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    2nd ordr homogenoues ODEs

    the behavoiur of the solution of d^2x/dt^2+adx/dt+4x
    depends on the value of a
    Note a=alpha

    a)find the ranges of a so that the solution displays

    i)overdamping
    ii)critical damping
    iii)underdamping(decaying oscilations)
    iv)growing oscilations
    v)constant oscilations

    b)For each of these cases, choose value of a within your stated
    ranges, and find the general solution, displaying your solution
    pictorially to show the behaviour of the solution

    c) By carefully considering all the possible values of a identify the ranes which do not lead to the behavouirs listed in a, and describe the typical behaviour in this case
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  2. #2
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    Re: 2nd ordr homogenoues ODEs

    Quote Originally Posted by Magical View Post
    the behavoiur of the solution of d^2x/dt^2+adx/dt+4x
    depends on the value of a
    Note a=alpha

    a)find the ranges of a so that the solution displays

    i)overdamping
    ii)critical damping
    iii)underdamping(decaying oscilations)
    iv)growing oscilations
    v)constant oscilations

    b)For each of these cases, choose value of a within your stated
    ranges, and find the general solution, displaying your solution
    pictorially to show the behaviour of the solution

    c) By carefully considering all the possible values of a identify the ranes which do not lead to the behavouirs listed in a, and describe the typical behaviour in this case
    You have not given an equation... I expect you meant \displaystyle \begin{align*} \frac{d^2x}{dt^2} + \alpha\,\frac{dx}{dt} + 4x = 0 \end{align*}.

    Anyway, I suggest you read this article.
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  3. #3
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    Re: 2nd ordr homogenoues ODEs

    thanks, how do u write the eqaution like that, wihout useing / or a?
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  4. #4
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    Re: 2nd ordr homogenoues ODEs

    We use the inbuilt LaTeX compiler. You can go to the LaTeX sub forum for more information
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