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quiz2 (1)

# quiz2 (1) - Massachusetts Institute of Technology...

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Massachusetts Institute of Technology Department of Ocean Engineering Department of Civil and Environmental Engineering 13.013J/1.053J Dynamics and Vibration Fall 2002 Quiz II “Closed book and notes”, two sheets of formulas allowed. Individual effort. Read all problems first. This quiz contains 7 printed pages.

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Figure for Problem 1: m m 1 k 2 m 2 k 1 c 2 v
Problem 1: (25 Points) At time t=0 a projectile of mass m and velocity v collides with mass m 1 and gets stuck to it. Just before the collision masses m 1 and m 2 are in static equilibrium and the springs k 1 and k 2 are unstretched. a) Using the direct method find the ordinary differential equations of motion after the collision. (10 Points) b) Using the indirect method find the ordinary differential equations of motion after the collision. (10 Points) c) What are the initial conditions for solving the resulting system of ordinary differential equations? (5 Points) 3

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Figure for Problem 2: L d d R x y E B A H z g D C G 4
Problem 2: (25 Points) A circular cylinder AB

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quiz2 (1) - Massachusetts Institute of Technology...

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