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Unformatted text preview: connecting them are constrained to move in a circle, so that each atom has just one (angular) degree of freedom. Show that the 0-frequency mode is a rotation about the center of mass. 2. A double pendulum (Fig. 1.4), consisting of masses m 1 and m 2 at the ends of rods of lengths l 1 and l 2 which are hinged at the location of m 1 , swings in the xz-plane. a) Write down the full Lagrangian in terms of the coordinates in Fig. 1.4, and the Lagrangian for small displacements about equilibrium. b) Find a transformation of coordinates, as done in class, which diagonalizes both the kinetic and potential energy terms. c) Describe the normal modes of vibration and the general solution for θ 1 and 2 , in terms of the initial angular displacements and velocities....
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This note was uploaded on 11/16/2010 for the course PHY 504 taught by Professor Staff during the Fall '08 term at Kentucky.
- Fall '08