# exam2 - 1.053J/2.003J Dynamics and Control I Fall 2007 Exam...

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1.053J/2.003J Dynamics and Control I Fall 2007 Exam 2 19 th November, 2007 Important Notes: 1. You are allowed to use two letter-size sheets (two-sides) of notes. 2. There are three problems totaling to 100 points. You have 80 minutes to solve them. 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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1. Sliding masses (30 points) An L-shaped rigid platform of mass M slides along the frictionless floor as shown in the figure below. The platform is connected to the fixed side walls by a mass-less spring of spring-constant k and a mass-less dashpot of damping-constant c . A smaller mass m slides along the horizontal edge of the platform without friction. As shown in the figure, the small mass is connected to the vertical edge of the platform by a mass-less spring of spring-constant k and a mass-less dashpot of damping-constant c . Constant horizontal force F is applied to the smaller mass. Determine the equation(s) of motion of the system using the Lagrangian approach. Assume that both the springs are initially un-stretched. c
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exam2 - 1.053J/2.003J Dynamics and Control I Fall 2007 Exam...

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