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ph2a_quiz1 - QUIZ1 ..Eachhasa...

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QUIZ 1 Two pendula pivot about an axis A and are constrained to remain in planes perpendicular to that axis. Furthermore the pivot points remain fixed. Each has a length L and a mass m . The angles from the vertical are θ 1 and θ 2 . (In the picture θ 1 <0 and θ 2 >0). The two pendula are coupled by a weak torsional spring that obeys Hooke's Law with torsional spring constant κ τ 2 = κ θ 2 θ 1 ( ) = τ 1 where τ 2 is the torque on mass 2 and τ 1 is the torque on mass 1. (a) [2.5 pts] Write down the linear coupled differential equations describing the motion of the pendula when the angles θ i 1 . (b) [2.5 pts] Find the two normal‐mode frequencies (eigenfrequencies).
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