Timeline for Show bigger amplitude of physical pendulum means bigger period
Current License: CC BY-SA 3.0
13 events
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| Feb 14, 2018 at 18:09 | comment | added | Chris♦ | @CarlWitthoft I'm aware. Your argument doesn't use this fact anywhere, though. It just asserts anything that starts higher up can obviously never catch up. Two marbles on the same cycloid slope started at different heights will always hit each other. | |
| Feb 14, 2018 at 13:16 | comment | added | Carl Witthoft | @Chris I'm familiar with the brachistochrone (and that it's a solution to the Principle of Least Action). The OP was talking specifically about a standard pendulum of unchanging length. | |
| Feb 14, 2018 at 7:28 | comment | added | Chris♦ | In a tautochrone pendulum, an object that starts higher does catch up, so your argument doesn't really work. | |
| Nov 20, 2017 at 15:45 | comment | added | sammy gerbil | Perhaps I am misunderstanding your answer. Are you arguing that intuition isn't reliable? I would agree with that. | |
| Nov 20, 2017 at 15:24 | comment | added | sammy gerbil | The larger amplitude pendulum has further to travel, but it accelerates faster. It is not intuitive which factor will win. As you concede, some math is required in order to decide. | |
| Nov 20, 2017 at 15:16 | comment | added | sammy gerbil | Fair point, it is not equivalent. However, I do not think it is intuitive/obvious that the larger amplitude pendulum cannot catch up. If the restoring force were exactly proportional to displacement then it would catch up at the equilibrium position (true SHM). For the simple pendulum the restoring force is less than proportional to displacement, so the larger-amplitude pendulum doesn't catch up. However, it is conceivable that restoring force could be greater than proportional to displacement, in which case the larger amplitude pendulum would overtake before the equilibrium point. | |
| Nov 20, 2017 at 14:40 | comment | added | Carl Witthoft | @sammygerbil That's a false equivalence. Just try to make marbles on any of those slopes catch up to another marble on the same slope. If your intuition suggests 'yes' to that or to the pendulum, you have serious disconnects with physical reality. | |
| Nov 18, 2017 at 0:45 | comment | added | sammy gerbil | -1 It is not intuitive that the pendulum with larger amplitude cannot catch up to that with smaller amplitude. eg See the counter-intuitive result of this experiment : Curved Slope faster than linear? | |
| Jan 12, 2015 at 18:55 | comment | added | Carl Witthoft | "faster can pass if it's moving faster" thanks for the tautology. I think you're missing my point, which was to show how easy it is to make major mistakes when using purely "intuitive" reasoning. | |
| Jan 12, 2015 at 18:51 | comment | added | Kevin Kostlan | The "hot water freezes faster" can't happen IF the entire system is described by one degree of freedom: the temperature. Real life hot water can freeze faster (cdn.phys.org/newman/gfx/news/hires/…) when the actual system is more complex. A pendulum bob has 2 degrees of freedom: force and velocity. A faster bob can surpass a slower one because velocities are different. Temperature does not have a "velocity term" appearing in the differential equation that governs it's change. Position does. | |
| Jan 12, 2015 at 18:45 | comment | added | Carl Witthoft | @Kevin - please edit so it's comprehensible; meantime, I'm not convinced your magnet situation gives the results you claim. | |
| Jan 12, 2015 at 13:55 | history | edited | Carl Witthoft | CC BY-SA 3.0 |
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| Jan 12, 2015 at 12:56 | history | answered | Carl Witthoft | CC BY-SA 3.0 |
