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ps7 - 1.053/2.003 Dynamics and Control I Fall 2006 Problem...

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1.053/2.003 Dynamics and Control I Fall 2006 Problem Set 7 Out: Monday, October 29 th , 2007 Due: Monday, November 5 th , 2007 1. Oscillating slender rod An L-shaped groove is shown in the figure below. Two ends of a slender rod of mass m and length L are attached to identical springs, each with a spring constant k . Both the springs are fixed to the L-shaped groove as shown in the figure below. Both the ends of the rod are constrained to move only along the L-shaped groove. Ignore gravity for this problem. Choose appropriate generalized coordinate(s) and derive the equation(s) of motion for this system using the Lagrangian approach. Cite as: Sanjay Sarma, Nicholas Makris, Yahya Modarres-Sadeghi, and Peter So, course materials for 2.003J/1.053J Dynamics and Control I, Fall 2007. MIT OpenCourseWare (http://ocw.mit.edu), Massachusetts Institute of Technology. Downloaded on [DD Month YYYY].
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2. Double pendulum A double pendulum is formed using two rigid, slender rods each of mass m and length l as shown in the figure below. Link 1 is free to pivot about point O and link 2 is free to
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