You can create a pendulum clock using the Tautochrone curve. That clock would always run at the same speed, no matter the size of the swing. It was invented by Christiaan Huygens in 1659. However, the added friction became a new problem.pic.twitter.com/qP6Ij8CDDu
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Thanks. Twitter will use this to make your timeline better. UndoUndo
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Looks a lot like the brachistocrone
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Yep, in fact it is close to being a bracistochrone.pic.twitter.com/j9r2TuJHSu
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I wonder if the same curve is dependent on the strength of gravity. IE would the same curve behave the same on Mars, Jupiter, or 3753 Cruithne?
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Yes, it would. Less gravity would just slow time. As long as you keep ignoring that the top of curve would have a different gravitational ‘constant’ than the bottom, it would work the same on any object.
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然而,作为科学家,必须要换位思考这么一个有趣的问题:如果不存在地球重力场,比如,在350公里高的国际空间站中,那么上述所有的结论,将成为一种谬论。对不对?
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怎麼會成為謬論
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its basically a pendulum without a pendulum
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It's actually not a pendulum; to think it is is to miss the Central point: it's a cycloid. Two identical penduli released from different points will definitely not arrive at the bottom at the same time!
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Only true for small oscillations though... The derivation of that relationship substitutes sin(x) for x to make it analytically solvable. A reasonable approach for small angles, but increasingly invalid for larger ones.
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