Assuming you have a vector of ‘T’ values that are functions of ‘s’, ‘g’ is given and the parameter to be estimated is ‘x’:
Tfcn = @(x,s,g) 2*pi*sqrt((x+s.^2)./(g.*s)); % Objective Function
s = 1:20; % Create Data
T = rand(size(s))*10; % Create Data
g = 9.81;
X0 = 1;
X = fminsearch(@(x) norm(T - Tfcn(x,s,g)), X0); % Estimate Parameters
figure
plot(s, T, '.')
hold on
plot(s, Tfcn(X,s,g), '-r')
hold off
grid
.
