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Unformatted text preview: Physics 318: First prelim exam Thursday, February 22, 2007 Duration: 90 minutes Instructions: Answer all questions. This is a closed book exam. There are 15 points for Q1, 15 for Q2 and 10 for Q3. 1. A pendulum which is exposed to gravity consists of a mass m which is suspended by means of a massless ideal elastic string of unextended length l and spring constant k . The ideal elastic string follows Hookes law like an ideal spring. The string is constrained by a frictionless fixture which still allows the string to extend, as shown in the figure. a. Calculate the kinetic and potential energies of the mass m , using the coordinates r , and indicated in the figure. Find the Lagrangian for this system. b. Find the equations of motion and quote them in the form: m r = . . . m = . . . m = . . . c. For this system there are two conserved quantities, functions of r , , , r , and . Derive expressions for these conserved quantities and explain their physical interpretation. 2.2....
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