11. A 120 in.-long beam AB is attached to the wall with a pin at point A and to a 66 in.-

long cable CD. A load lb is attached to the beam at point B. The tension in the cable T and the x and y components of the force at A ( and ) can be calculated from the equations:

where L and are the lengths of the beam and the cable, respectively, and d is the distance from point A to point D where the cable is attached.

(a) Use MATLAB to solve the equations for the forces T, , and in terms of

d, L, , and W. Determine given by .

(b) Use the subs command to substitute lb, in., and in. into the expressions derived in part (a). This will give the forces as a function of the distance d.

(c) Use the ezplot command to plot the forces T and (both in the same figure as functions of

d, for d starting at 20 and ending at 70 in.

(d) Determine the distance d where the tension in the cable is the smallest.

Determine the value of this force.