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Math Help - System Modeling and integration problem. Need help?

  1. #1
    Newbie
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    Mar 2009
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    Distance between the plates: Integration problem

    There are two plates, green and blue as shown in the diagram below.



    The green plate can move, due to which the distance R between the plates changes.

    R at a height of h will be

    R=(H d2+∆d1 h)/H

    What will be the equation for integral of R for complete height H. Please explain the solution. I tried to solve it but came up with log(H)-log(0) in the equation. Log 0 cannot be solved.

    Thankyou for your help
    Last edited by Oscar6330; March 22nd 2009 at 08:32 PM.
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  2. #2
    MHF Contributor
    Joined
    Nov 2008
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    France
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    Hi

    Not sure to have well understood your question
    Anyway ...
    If you want to calculate the mean distance between the two plates

    \frac1H\int_{0}^{H}\left(d_2+\frac{\Delta d_1}{H}\:h\right)dh=d_2+\frac{\Delta d_1}{2}

    But this can be found geometrically without using integrals
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