ENG102_HW5

ENG102_HW5 - t ) of the united mass after the collision....

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DATE: October 23, 2011 DUE: October 28, 2011 ENG102, homework set #5. x m 1 m 2 v 2 x=0 k Look at the figure above. We consider a harmonic oscillator consisting of a spring with spring constant k , connected to a wall at one end and a mass m 1 at the other. The mass can move along the x -axis as indicated. The coordinate of the mass is such that x = 0 when the spring is without tension. At time t = 0 the mass is at rest at x = 0 . At this time ( t = 0 ) another mass m 2 m 1 hits m 1 with velocity v 2 . The quantities listed here are considered known, as is the friction coefficient α mentioned below. Use the results from HW4. 1. We assume that there is a friction force between m 1 and the horizontal surface, such that the force on m 1 is f f = - α ˙ x . We further assume that the collision between m 1 and m 2 is instantaneous and inelastic such that the two masses move as one after the collision. a. Write the equation of motion for the united object after the collision. b. Determine x (
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Unformatted text preview: t ) of the united mass after the collision. Specify the smallest value of x ( t ) and the frequency of motion. 2. We assume that there is a friction force between m 1 and the horizontal surface, such that the force on m 1 is f f =- x . We further assume that the collision between m 1 and m 2 is instantaneous and elastic. a. Write the equation of motion for m 1 after the collision. b. Determine the trajectory x 1 ( t ) of m 1 after the collision, and specify the oscilla-tion frequency. c. Write the equation of motion for m 2 after the collision, assuming that the same friction coefficient applies to the two masses. d. Determine the trajectory x 2 ( t ) of m 2 after the collision. Niels Grnbech Jensen DEPARTMENT OF MECHANICAL AND AERONAUTICAL ENGINEERING | UNIVERSITY OF CALIFORNIA | DAVIS, CALIFORNIA 95616 TEL: 530.752.5335...
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