Two simple pendulums with equal lengths (L = 0.956m) and masses (m = 0.426kg) are separated...

  

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Two simple pendulums with equal lengths (L = 0.956m) and masses (m = 0.426kg) are separated by a distance D = 0.43m. The masses are connected to each other by a spring with un-compressed length D and spring constant k = 8.35N/m. This is illustrated in the image below, where measures the angular displacement of the left pendulum and 2 measures the angular displacement of the right pendulum. D L L www.e m k m When the masses are set into simple harmonic motion, the spring and pendulum work as a coupled harmonic oscillator. Solving Newton's Laws for the two pendulum gives the coupled harmonic oscillator equation: d dt2 -01 -02 m 01 - (01-02) (02-01) = -- The two natural modes of the system are when the pendulum are moving in the same direction, 0 = 01 +02, and when they are moving in opposite directions 0 = 01-02 The two natural (angular) frequencies of the system are w and wh. What is numerical value of the larger w for the system? S-1 Two simple pendulums with equal lengths (L = 0.956m) and masses (m = 0.426kg) are separated by a distance D = 0.43m. The masses are connected to each other by a spring with un-compressed length D and spring constant k = 8.35N/m. This is illustrated in the image below, where measures the angular displacement of the left pendulum and 2 measures the angular displacement of the right pendulum. D L L www.e m k m When the masses are set into simple harmonic motion, the spring and pendulum work as a coupled harmonic oscillator. Solving Newton's Laws for the two pendulum gives the coupled harmonic oscillator equation: d dt2 -01 -02 m 01 - (01-02) (02-01) = -- The two natural modes of the system are when the pendulum are moving in the same direction, 0 = 01 +02, and when they are moving in opposite directions 0 = 01-02 The two natural (angular) frequencies of the system are w and wh. What is numerical value of the larger w for the system? S-1