clear; clc
display('Chung,  Karl 660781774')
display('Problem 1')
display('Part A')
A=[3 -3 7 1;
    -2 6 0 5;
    1 4 -3 3;
    4 -3 -2 5];
B=inv(A);
display('Determanint of A =')
det(A)
display('Determanint of A^-1 =')
det(B)
display('Part B')
for t=1:1:5
    A=[3 -1 6 4 2;
    4 3 -2 1 6;
    -2 -4 5 -3 -2;
    7 1 0 5 -1;
    3 9 8 -2 4];
B=det(A);
    A(1,t)=35;
    A(2,t)=61;
    A(3,t)=-41;
    A(4,t)=1;
    A(5,t)=87;
    C=det(A);
    D(t)=C/B;
end
D';
display('X1=')
D(1,1)
display('X2=')
D(1,2)
display('X3=')
D(1,3)
display('X4=')
D(1,4)
display('X5=')
D(1,5)

display('Problem 2')

for theta=0:1:90
    n=[0 0 1];
   raw=[.1*sind(theta) -.1*cosd(theta) 0];
   Fw=[0 -9.81*20 0];
   rac=2*raw;
   cd=[.2-.2*sind(theta) .1+.2*cosd(theta) .125];
   CD=cd/norm(cd);
   %CD = force vector of wire
   wcross=cross(raw,Fw);
   Mw=dot(wcross,n);
   tcross=cross(rac,CD);
   Mt=dot(tcross,n);
   T=-Mw/Mt;
   M(theta+1)=T/9.81;
   g10(theta+1)=10;
    
end
figure(1)
plot(0:1:90,M)
xlabel('Theta Degrees')
ylabel('Mass (kg)')
title('Mass Required for Equilibrium')
w=abs(g10-M);
display('For mass of 10kg')
[diff_w,theta]=min(w)

display('Problem 3')
hold off
Theta=[0]
Wc=12000; Wb=600; Wl=3600; A=zeros([0])
for theta=0:1:800
    Theta(1,theta+1)=theta/10;
    d(1,theta+1)=(9*Wc-12*Wb*cosd(theta/10)-25*cosd(theta/10)*Wl)/(Wc+Wl+Wb);
    alpha=90-(theta/10);
    beta=(theta/10)-atand((25*sind(theta/10)-6)/(14+25*cosd(theta/10)));
    tens=(sind(alpha)*(12*Wb+25*Wl)-25*sind(beta)*Wl)/(24*sind(beta));
    G=theta/10-beta;
    Ax=tens*cosd(G);
    Ay=Wb+Wl+tens*sind(G);
    B=[Ax, Ay];
    Ar(1,1+theta)=norm(B);
    W(1,1+theta)=(8*Wc-(12*cosd(theta/10)+1)*Wb)/(25*cosd(theta/10)+1);
end
figure(2)
plot(Theta,d)
xlabel('Theta Degrees')
ylabel('Distance (ft)')
title('Location of resultant force')
figure(3)
plot(Theta,Ar)
xlabel('Theta Degrees')
ylabel('Reaction at A (lb)')
title('Reaction at A as a function of Theta')

% Problem 4
hold on
disp('Problem 4')
for a=5:1:500
    ac(1,a)=a;
    p(1,a)=(4750*a)/(800-a);
    b(1,a)=(1583.33*a)/(800-a);
end
figure(4)
plot(ac,p)
 xlabel('Location of A (mm)')
ylabel('Force (N)')
title('Minimum force required to prevent motion')
figure(5)
 plot(ac,b)
 xlabel('Location of A (mm)')
ylabel('Force (N)')
title('Minimum force required to prevent motion')