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+// SAMPLE PROBLEM 6/3

+clc;funcprot(0);

+// Given data

+W_b=644;// lb

+r_i=12;// inch

+r_o=24;// inch

+theta=45;// degree

+P=400;// lb

+k_o=18;// inch

+W=322;// lb

+g=32.2;// lb

+

+// Calculation

+// Solution 1

+// I=k^2*m

+Ibar=(k_o/12)^2*(W/g);// lb-ft-sec^2

+function[X]=acceleration(y)

+// SigmaM_G=Ibar*alpha

+    X(1)=((P*(r_o/12))-(y(1)*(r_i/12)))-(Ibar*y(2));

+// SigmaF_y=m*a_y

+    X(2)=((y(1)-W_b))-((W_b/g)*y(3));

+// a_t=r*a;

+    X(3)=y(3)-((r_i/12)*y(2));

+endfunction

+y=[100 1 1];

+z=fsolve(y,acceleration);

+T=z(1);// lb

+alpha=z(2);// rad/sec^2

+a=z(3);// ft/sec^2

+// SigmaF_x=0

+O_x=P*cosd(theta);// lb

+// SigmaF_y=0

+O_y=W+T+(P*sind(theta));// lb

+O=sqrt(O_x^2+O_y^2);// lb

+printf("\nSolution I:T=%3.0f lb,alpha=%1.2f rad/sec^2,a=%1.2f ft/sec^2,O=%4.0f lb",T,alpha,a,O);

+// Solution 2

+function[Y]=acceleration(x)

+// SigmaM_o=(Ibar*alpha)+(m*abar*d)

+    Y(1)=((P*(r_o/12))-(W_b*(r_i/12)))-((Ibar*x(1))+((W_b/g)*x(2)*(r_i/12)));

+// a_t=r*a;

+    Y(2)=x(2)-((r_i/12)*x(1));

+endfunction

+x=[1 1];

+m=fsolve(x,acceleration);

+alpha=m(1);// rad/sec^2

+a=m(2);// ft/sec^2

+// SigmaF_y=Sigmam*(a_ybar)

+O_y=(W+W_b+(P*sind(theta)))+(((W/g)*(0))+((W_b/g)*alpha));// lb

+// SigmaF_x=Sigmam*(a_xbar)

+O_x=P*sind(theta);// lb