quiz2 - A disk of radius r and mass M is placed on a fixed...

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Fall 2004 2.032 DYNAMICS Quiz No.2 Wednesday, December 8, 2004 This is a CLOSED-BOOK, Open notes Quiz. Problem 1 (20 points) Two small masses, m 1 and m 2 , are constrained to move in a vertical plane by two inextensible strings, as shown in figure 1. The lengths of the two strings are R and L = ρ + r , respectively. There is a force of magnitude F acting on the mass m 2 , with its line of attack always parallel to the string attached to m 2 . The constant of gravity is g . The pulley shown in the figure is small and frictionless. (a) Classify all constraints and forces (give reasoning). Determine the number of degrees of freedom. (b) Derive the Lagrangian equations of motion in terms of φ 1 and 2 . L m 1 R 1 r m 2 F 2 g Figure 1
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Problem 2 (20 points)
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Unformatted text preview: A disk of radius r and mass M is placed on a fixed tube of radius R , as shown in Figure 2. The center of the disk is at a distance l from the ceiling and is attached to the ceiling through a spring of stiffness k 1 and unstretched length l . At the same time, a block of mass m is hanging from the center of the disk on a spring of stiffness k 2 and unstretched length l . We assume that the disk cannot slip on the tube and the lower spring remains vertical on any motion of the system. The constant of gravity is g . Without deriving equations of motion, find sufficient and necessary conditions for the stability of the equilibrium shown in Fig. 2. r m R k 2 Figure 2 l k 1 g...
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quiz2 - A disk of radius r and mass M is placed on a fixed...

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