Exam 2 2.003 Dynamics and Vibrations This is a closed book quiz. Each student may bring two, sides of an 8; x 11 inch sheet of self-prepared notes. Problem 1 (lOpts) Collar B can slide along rod AC and is attached by a pin to a block that can slide in the vertical slot shown. The block is acted upon by a force P and a torque M is applied to the rod AC at the pivot point A. All sliding and rotating contacts are frictionless. (i) Determine the generalized force conjugate to the generalized coordinate 0. (ii) State the principle of virtual work and apply this ; princi determine the torque M required to maintain equilibrium. Cite as: Thomas Peacock, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Problem 2 (10 pts) - - A cart of mass ,V is attach( le wall by a spring k. A T-shaped body consisting of two long, thin bars of mas ld length L is pinned to thc center of the cart, as shown in figure 2. Find the equations of motion of the system in terms of t,he generalized coordinates x and 3 using Lagrange's equations. - Cite as: Thomas Peacock, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].Problem 3 (lOpts) A bead of mass rn can slide freely along a taut string as shown in figure 3. Find e equilibrium position of the bead for R =constant, id determine the stability of e equilibrium. ththFigure 3 Cite as: Thomas Peacock, course materials for 2.003J/1.053J Dynamics and Control I, Spring 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month
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