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Homework Help: Hyperbolic Cosine curve fitting

  1. Apr 24, 2010 #1
    1. The problem statement, all variables and given/known data
    I need to fit a curve using cosh to a hyperbola with a vertex of (0,0) and a point at (4,7).

    The scanned worksheet can be found here
    http://img519.imageshack.us/i/scan0001gu.jpg/" [Broken]
    http://img192.imageshack.us/i/scan0002uz.jpg/" [Broken]

    2. Relevant equations
    [tex]y=a cosh (\frac{x}{a})-a=\frac{a}{2}(e^{\frac{x}{a}}+e^{\frac{-x}{a}})-a[/tex] "is the formula for a hyperbola at a vertex of 0,0. a is a constant that modifies the shape" that is what the assignment said exactaly


    3. The attempt at a solution
    I plugged in 4 for x and 7 for y and attempted to solve algebraically, I just got stuck. then I plugged the equation I attempted to solve into wolfram alpha and got the response no integer solution.

    http://www.wolframalpha.com/input/?i=7%3D(a/2)(e^(4/a)%2Be^(-4/a))%2Ba+solve+for+a
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 24, 2010 #2
    The solution value of a isn't an integer.

    Try graphing the function

    [tex]
    y=x cosh (\frac{4}{x})-x-7
    [/tex]

    and use that to help you find the right value of a.
     
  4. Apr 24, 2010 #3
    There is probably no closed-form solution, and besides, this formula doesn't describe a hyperbola, but a catenary.
     
  5. Apr 25, 2010 #4
    Thanks so much for your help! I graphed that, and since you solved to equation for 0 then turned 0 into y I looked for the x intercept of the graph and the value fit, thank you so much!
    But just for the sake of knowing, how can you guys tell if an equation has no closed form solution?
     
    Last edited: Apr 25, 2010
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