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final_exam

# final_exam - MEE 201 Advanced Dynamics Fall 2007 Final Exam...

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MEE 201 Advanced Dynamics, Fall 2007: Final Exam 12/7//2007 Exam is take home, open notes, books and homeworks, no internet please. It is due Friday, 12/14/2007 to Melecia Valdez in the front office of Mechanical and Environmental Engineering Department, before the office closes. You can take as much time as you need to complete it. Include a printout of your code for problems that include numerical simulation. 1. Consider the system shown in figure 1. The mass M is constrained to move vertically, the mass on the pendulum is m 6 = M and the mass of the rod and the spring are neglected. The spring is a nonlinear, stiffening spring with spring force given by kx + k s x 3 , k and k s are different constants. There is no friction. Gravity is acting straight down. Figure 1: (a) Derive the equations of motion for the system using the Lagrangian approach. The spring is assumed to have equilibrium length l eq = 0. 1

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(b) Assume the angular velocity of the pendulum, ω , is given and constant in time. Derive the resulting equation of motion for the mass
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final_exam - MEE 201 Advanced Dynamics Fall 2007 Final Exam...

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