• Support PF! Buy your school textbooks, materials and every day products Here!

Hyperbolic Cosine curve fitting

  • Thread starter Denyven
  • Start date
  • #1
19
0

Homework Statement


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]

Homework 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


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:

Answers and Replies

  • #2
351
1
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.
 
  • #3
59
0
There is probably no closed-form solution, and besides, this formula doesn't describe a hyperbola, but a catenary.
 
  • #4
19
0
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.
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:

Related Threads for: Hyperbolic Cosine curve fitting

  • Last Post
Replies
1
Views
873
  • Last Post
Replies
8
Views
3K
Replies
1
Views
3K
Replies
4
Views
1K
Replies
1
Views
2K
Replies
4
Views
1K
  • Last Post
Replies
10
Views
3K
Top