A classical problem in engineering is the Catenary problem. This problem is an idealized model of the static equilibrium of a rope or chain suspended from 2 points. The solution to the problem is
y = a*cosh(x/a)
where a is a constant to computed and x ∈ (−h/2, h/2). If, additionally, you are given the length of the suspended rope, L, the following equation needs to be solved to compute the constant a:
L= (2a)*sinh (h/2a)
Assuming h = 97 and L = 100, use a Newton solver to compute a. Compare with using MATLAB’s fzero command. Plot the resulting Catenary curve.