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Unformatted text preview: PHYS 3202 Classical Mechanics II - Homework #7 Due at 12:05pm, Friday March 18, 2011 in the class Please show intermediate steps of your calculations. Whenever appro- priate, you may draw diagram(s). Problem 1 (5 points): a particle undergoing periodic motion in a conservative force field traces out a symplectic area A = Z p d r in each period . The particles kinetic energy is T . If the particles speed is much smaller than the speed of light in vacuum, show that A = 2 h T i , where h T i is the average kinetic energy in each period: h T i 1 R Tdt . (To prevent confusion with the kinetic energy, we use symbol for the period.) Problem 2 (15 points): For each of the following 3 systems, compute the energy E as a function of the symplectic area A = R p d r within each period , and check whether E A (if yes, give the value of ). For each system, also compute the frequency of the motion 1 / , and then verify the relation = E ( A ). Omit gravity. For system 2, please eliminate the radius...
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