HW12 prob1_GPS19_G13

HW12 prob1_GPS19_G13 - GPS 5-19 or Goldstein 5-13 This problem is distantly related to the Spring-Pendulum Problem from Ch 1 but here the spring is

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GPS 5-19 or Goldstein 5-13 This problem is distantly related to the Spring-Pendulum Problem from Ch. 1, but here, the spring is constrained to oscillate vertically and the mass point is expanded into a rigid rod of mass M and length 2 l that swings in a vertical plane. One end of the rod is attached to the spring. Because the motion of the bar is con f ned to a plane, the system has only two degrees of freedom: the vertical displacement of the spring, y , and the angular displacement of the rod from the vertical, θ . The angle θ will be measured from a y axis that is positive in the downward direction so that θ is positive when the mass point is displaced away from its rest position. The x axis is perpendicular to the y axis and is positive to the right. Let’s f rst consider the potential energy. The contribution from the spring is simply 1 2 ky 2 . The gravitational contribution can be worked out as follows. Imagine that the rod is at an angle

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This note was uploaded on 12/19/2010 for the course PHYSICS ph 409 taught by Professor Wilemski during the Fall '10 term at Missouri S&T.

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HW12 prob1_GPS19_G13 - GPS 5-19 or Goldstein 5-13 This problem is distantly related to the Spring-Pendulum Problem from Ch 1 but here the spring is

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