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Problem set 4 for phys601, due on october 3, 2008, based on chapters 2, questions 10, 12, 18, 24, and 26 from goldstein et al. The set includes a qualifier problem and an additional problem with parts c and d. Students are required to check their answers by verifying the limits at θ = 0 and θ = π/2 and use the assumption of solutions of the form qj = qj0 exp[-iωt] to find the general solution of the equations of motion.
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From Goldstein et al Do Ch 2 #s 10, 12, 18, 24, 26
4.1Q (Qualifier Problem)
4.2Q (adapted from Qualifier Problem, attached)
Add these to the problem:
c. Check your answer by making sure that the limits θ = 0 and θ = π/2 make sense.
d. A set of linear, coupled ODEs with variables qj (t), j=1,…,n, can always be solved by assuming solutions of the form qj = q (^) j0 exp[-iωt] provided the coefficients of each of the terms are constant. Use this to find the general solution of your equations of motion.