Unformatted text preview: (22) Calculate the turning point θ min and θ max for the spherical pendulum of the midterm for the special case mgR = M 2 z / (4 mR 2 ) = E/ 2. Due in class (6 points). Read Chapter V of LandauLifshitz up to § 26, p.79. (23) Derive the results of problem 3 § 21 of Landau and Lifshitz (frequency of oscillations). Due October 26 before class (4 points). (24) Calculate a and α of Eq. (22.4 and 1/2) of Landau and Lifshitz in terms of a and α of Eq.(22.4) of Landau and Lifshitz. Then, let γ = ω + ± . Taylor expand x ( t ) = a cos( ω t + α ) + f [cos( γ t + β )cos( ω t + β )] m ( ω 2γ 2 ) to order ± and take the limit ± → 0. Due in class (4 points). Now October 28 before class. (25) Calculate the normal modes (eigenfrequencies) of the pendulum of problem 8, set 2. Due October 31 before class (4 points)....
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 Fall '11
 berg
 mechanics, Work, 1966, 1973, Landau

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