HW4_Work

setdefaults;

m = 0.5; % mass in kg
g = 9.81; % acceleration due to gravity m/s^2
K = 30;  %spring constant N/m

%Part a

collar_potential_energy = @(x_C, theta) m*x_C*g*sin(theta) + .5*K *((0.5 - sqrt(0.5^2+(0.5-x_C)^2)))^2;

%Part b

theta = 0;

[x1,fx1,ea1,iter1] = goldmin(collar_potential_energy,-10,10,0.0001,100,theta);

%Part c

theta = .9*pi/180;  
thetaVec = linspace(0,pi, 400);
fx2 = 0;

[x3,fx3,ea3,iter3] = goldmin(collar_potential_energy,-10,10,0.0001,100,theta);

for i = 1:length(thetaVec)
    theta = thetaVec(i);
[x2, fx2(i), ea2, iter2] = goldmin(collar_potential_energy, -10, 10, 0.0001, 100, theta);
end

plot(thetaVec, fx2);
    title('Plot of Minimum PE for x_C with given Angle');
    xlabel('Theta (radians)');
    ylabel('x_C (meters)');