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Unformatted text preview: Physics 523 Final Exam, Fall 2009 Monday, January 18, 1:30-4:30pm This exam consists of 5 problems (with multiple parts) on 2 pages, with a total of 100 pts. Do all problems, answered in the exam booklet provided, and clearly show all your work. This is a closed-book exam. Non-programmable calculators may be used (though should not be necessary). Remember to write your name in the exam booklet, and write and sign the pledge : I pledge my honor that I have not violated the Honor Code during this examination. Problem 1. [14 pts total] In Minkowski spacetime ds 2 =- dt 2 + dx 2 + dy 2 + dz 2 , a particle undergoes simple harmonic motion given by x ( t ) = A cos( t ). (a) [6 pts] What is the 4-velocity u of the particle? (b) [2 pts] For a fixed frequency , what is the maximum amplitude A m of oscillation A so that the particle is never spacelike? (c) [6 pts] For a particle that has exactly the maximum amplitude A m calculated in part (b), what is the total proper time of one oscillation as measured in the particles rest frame?what is the total proper time of one oscillation as measured in the particles rest frame?...
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