exam1 - 1.685512.0345118.377J Nonlinear Dynamics and Waves...

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Take-Home Exam Thursday, April 5,2007 This is a closed-book exum. You may use your own class notes, problem sets and solutions posted on the 1.685/2.034/18.377 website only. You are not allowed to discuss this exum with anyone else. If you need clarification regarding the problems, please ask me. The exam is due on Tuesday,l loth, 2007 before 5:00pm, Problem 1 (10 points) A particle of mass m is constrained to move around a smooth circular wire of radius a fixed in a vertical plane. The particle is acted on by gravity and is attached to one end of a linear I(< the other end being fixed to the highest (a) Derive the governing equations of motion. (b) Find the number of equilibrium points and discuss their stability as k varies. (c) Sketch the bifurcation diagram describing these equilibrium states as a function of k. (d) Sketch the phase plane for representative values of k. Problem 2 (10 points) The motion of a particle restrained by a linear spring and under the combined influence of
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.034J taught by Professor Triantaphyllosakylas during the Spring '07 term at MIT.

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exam1 - 1.685512.0345118.377J Nonlinear Dynamics and Waves...

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