% Hanging cable problem

d0 = input('Enter distance between supports (try 100) ');
h0 = input('Enter sag height of cable (try 10) ');

f = @(lambda,h,d) lambda*cosh(d/2/lambda) - lambda - h;
F = @(lambda) f(lambda,h0,d0);

guess = d0^2/(8*h0);

% Try secant method to find lambda

lambda = secant(F,guess, guess*1.1, 1e-5, 15, true)

% Try it using Matlab's fzero

lambda = fzero(F, guess)

% Now find arc length using exact formula for integral

arc_length = 2 * lambda * sinh(d0/(2*lambda))