ENG102_HW4

ENG102_HW4 - c. Determine x ( t ) of the united mass after...

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DATE: October 16, 2011 DUE: October 21, 2011 ENG102, homework set #4. 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. 1. We assume that there is no friction between m 1 and the horizontal surface, and 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. Express the velocity u 12 of the united object immediately after the collision, and calculate the loss in kinetic energy during the collision. b. Write the equation of motion for the united object after the collision.
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Unformatted text preview: c. Determine x ( t ) of the united mass after the collision. Specify the amplitude and frequency of the motion. 2. We assume that there is no friction between m 1 and the horizontal surface, and that the collision between m 1 and m 2 is instantaneous and elastic. a. Find the two velocities u 1 and u 2 immediately after the collision (hint: do cal-culations in center-of-mass coordinate system). b. Write the equation of motion for m 1 after the collision. c. Determine the trajectory x ( t ) of m 1 after the collision, and specify oscillation amplitude and frequency. 3. What is the SI unit of k ? Niels Grnbech Jensen DEPARTMENT OF MECHANICAL AND AERONAUTICAL ENGINEERING | UNIVERSITY OF CALIFORNIA | DAVIS, CALIFORNIA 95616 TEL: 530.752.5335...
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