{"id":100,"date":"2020-04-13T18:58:43","date_gmt":"2020-04-13T18:58:43","guid":{"rendered":"https:\/\/wp.physics.wisc.edu\/ingersollmuseum\/?page_id=100"},"modified":"2026-05-13T06:20:42","modified_gmt":"2026-05-13T06:20:42","slug":"coupledpendulums","status":"publish","type":"page","link":"https:\/\/wp.physics.wisc.edu\/ingersollmuseum\/exhibits\/mechanics\/coupledpendulums\/","title":{"rendered":"Coupled Pendulums"},"content":{"rendered":"

Coupled Pendulums<\/h1>\n\n\n
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What To Do<\/h2>\n\n\n\n
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  1. Pull one pendulum toward you.<\/li>\n\n\n\n
  2. Release the pendulum!<\/li>\n<\/ol>\n\n\n\n

    WHAT HAPPENS TO THE TWO PENDULA AFTER ABOUT 30 SECONDS <\/u><\/strong><\/p>\n\n\n\n

    OR 20 OSCILLATIONS (Count them!)?<\/u><\/strong><\/p>\n\n\n\n

    Answer:<\/strong> The amplitude of the second pendulum increases while the amplitude of the first decreases. The first pendulum eventually stops while the second has a large amplitude. Then the situation is reversed as the second pendulum begins to drive the first.  The amplitude of the second pendulum decreases while the amplitude of the first increases again.<\/p>\n\n\n\n

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    (Front View)<\/center><\/figcaption><\/figure>\n<\/div>\n\n\n\n
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    What is Happening?: <\/u><\/strong><\/p>\n\n\n\n

    Energy<\/strong> is transferred between the pendula by the coupling spring<\/strong> that connects them. The oscillation of the second pendulum is being driven by the first.<\/p>\n<\/div>\n<\/div>\n\n\n\n

    An Explanation: <\/u><\/strong><\/p>\n\n\n\n

    The motion of the two pendula can be thought of as the superposition (combination) of two simple motions or normal modes.<\/p>\n\n\n\n

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    (Side View)<\/center><\/figcaption><\/figure>\n<\/div>\n\n\n\n
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    Motion 1: <\/strong><\/p>\n\n\n\n

    The pendula move side-by-side in phase.  The coupling spring transmits no force.  The period of the coupled pendula equals that of each pendulum if they were not connected.<\/p>\n<\/div>\n<\/div>\n\n\n\n

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    (Side View)<\/center><\/figcaption><\/figure>\n<\/div>\n\n\n\n
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    Motion 2: <\/strong><\/p>\n\n\n\n

    The pendula move in exact opposition, 180o<\/sup> out of phase. The coupling spring exerts an additional (restoring) force which tends to bring the pendulum to it\u2019s rest position, increasing each pendulum\u2019s speed, and thus shortening the period slightly.  Because of this difference in periods, the two normal motions get progressively out of step.<\/p>\n<\/div>\n<\/div>\n\n\n\n

    Physics Lecture Demonstration Database<\/a> <\/b><\/i><\/p>\n\n\n\n