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Math Help - Rearrangement of Zhang's Equation

  1. #1
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    Rearrangement of Zhang's Equation

    Hello. I am having trouble rearranging this equation:

    Q=\frac{\pi t f_p f_m^2}{2(f_m^2 - f_p^2)}

    to get an equation for f_p in terms of t. Only f_p and t are variables, the other symbols are constants.

    I think I have got it as far as:

    \frac{f_p}{f_m^2}-\frac{1}{f_p}=\frac{-\pi t}{2Q}

    reasonably safely, but am not sure where to go from there! This looks distinctly like it should be quite do-able, but has been frustrating me all morning..

    Any help would be appreciated.
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  2. #2
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    Quote Originally Posted by stealthbadger View Post
    Hello. I am having trouble rearranging this equation:

    Q=\frac{\pi t f_p f_m^2}{2(f_m^2 - f_p^2)}

    to get an equation for f_p in terms of t. Only f_p and t are variables, the other symbols are constants.

    I think I have got it as far as:

    \frac{f_p}{f_m^2}-\frac{1}{f_p}=\frac{-\pi t}{2Q}

    reasonably safely, but am not sure where to go from there! This looks distinctly like it should be quite do-able, but has been frustrating me all morning..

    Any help would be appreciated.
    Streamline things a bit:

    Q = \frac{A f_p}{B - f_p^2}

    and it should be obvious what the constants A and B represent.

    Then:

    QB - Qf_p^2 = A f_p \Rightarrow Q f_p^2 + A f_p - QB = 0.

    Solve the quadratic for f_p and then substitute the appropriate expressions for A and B.
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  3. #3
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    I did this initially, but t is not a constant, so I didn't think that it was valid?
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  4. #4
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    Quote Originally Posted by stealthbadger View Post
    I did this initially, but t is not a constant, so I didn't think that it was valid?
    It is.
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