Problem 2 (15 pts): Figure 2 shows a system in which force f pushes the mass my and causes a displacement of 21 and 22 to masses mi and m2, respectively. As is shown in this figure, the force f is applied to the mass my with an angle of 30 and it is assumed that both masses are moving in the upward direction. The friction coefficient between each of the masses m and m, and the slope are equal to p and respectively. The friction forces are proportional to the pressing force normal to the slope. 122 www b 1122 x2 sa www 11 mi 30 Figure 2: Schematic of the mechanical system to model in Problem 2. Your tasks: A Draw the free body diagram for each of the masses m, and m (10 pts). B Derive the equations of motion for the system of masses (5pts). Problem 3 (15 pts): In the system shown in Figure 3, two springs and a damper connect rolling solid disk with the mass of M and moment of inertia of I, to fixed walls. The disk rolls without slipping and has two different thicknesses resulting in two different radii. The springs and the damper are hooked to the points depicted in the figure. The small angle assumption is valid as the points P and Q are approximately vertical over the center of the disk at point O. tim lo. M Figure 3: Schematic of the mechanical system to model in Problem 3. Your tasks: A Draw the free body diagram of the disk. (7 pts). B Extract the equation of motion of the disk as a function of the horizontal position of the center of mass, z. (8 pts.)