{"id":5154,"date":"2023-12-15T17:02:08","date_gmt":"2023-12-15T17:02:08","guid":{"rendered":"https:\/\/www.betrisey.ch\/synchronisations-de-3-pendules-de-foucault"},"modified":"2025-01-28T06:49:20","modified_gmt":"2025-01-28T06:49:20","slug":"synchronisations-de-3-pendules-de-foucault","status":"publish","type":"page","link":"https:\/\/www.betrisey.ch\/en\/synchronisations-de-3-pendules-de-foucault","title":{"rendered":"Synchronisation of 3 Foucault pendulums"},"content":{"rendered":"\n\n<p class=\"wp-block-paragraph\"><strong>Improbable experiment posted live&#8230;.<\/strong><\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">The idea for this experiment came to me in 2002 in my studio when I saw <strong>two Foucault pendulums hanging from the same concrete ceiling, their rotations remaining perfectly synchronous for a whole month.<\/strong> They had been doing this for perhaps a year without me noticing. This couldn&#8217;t have happened by chance, so what was the law that made them rotate together?<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">So here was a triple experiment to synchronise the rotations of small Foucault pendulums swinging freely against the same wall, the aim being to discover what would happen between the 5 choices available when they were initially thrown in the same direction:<\/p>\n\n\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color wp-elements-b36fc77e5ecd76869b92c4088af40963 wp-block-paragraph\">1) <strong>Anarchy<\/strong>: everyone goes their own way, ignoring the other.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Or<\/p>\n\n\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color wp-elements-509ae6b1e54fb819316c6316892460f7 wp-block-paragraph\">2) <strong>Love<\/strong>: they synchronise their rotations and always oscillate on the same parallel plane.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Or<\/p>\n\n\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color wp-elements-2a330bd1ddc5b9015cccd7f066c0fa5c wp-block-paragraph\">3) <strong>Dictatorship<\/strong>: they start to oscillate in the same plane, then the heaviest one kills the other by successive phases and phase shifts.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Or <\/p>\n\n\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color wp-elements-f5a6c557b3d75b5ffbfa25d87708cb5c wp-block-paragraph\">4) <strong>Cold war<\/strong>: they choose the plane of oscillation most opposed to the other (90\u00b0 for 2 pendulums, 120\u00b0 for 3 pendulums) and maintain it indefinitely.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Or else&#8230; <\/p>\n\n\n\n\n\n<p class=\"has-vivid-red-color has-text-color has-link-color wp-elements-b8220847bd397b65dfee11ecb435f6b1 wp-block-paragraph\">5) <strong>&#8230;<\/strong> <strong> There&#8217;s something else<\/strong> we&#8217;re going to have to find out.<\/p>\n\n\n\n<div class=\"wp-block-image\">\n\n<figure class=\"aligncenter size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"571\" height=\"1024\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/test-synchro-571x1024.jpg\" alt=\"\" class=\"wp-image-2900\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/test-synchro-571x1024.jpg 571w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/test-synchro-167x300.jpg 167w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/test-synchro-768x1377.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/test-synchro-856x1536.jpg 856w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/test-synchro-1142x2048.jpg 1142w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/test-synchro-scaled.jpg 1427w\" sizes=\"auto, (max-width: 571px) 100vw, 571px\" \/><\/figure>\n<\/div>\n\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-2c73b5eb7a2b3ef13c005db228ee9594 wp-block-paragraph\"><strong>Experiment n\u00b01, December 2023 <\/strong><\/p>\n\n\n\n\n\n<p class=\"has-black-color has-text-color has-link-color wp-elements-4a39bf800eaf30626043d34ffd4db73f wp-block-paragraph\">This experiment was not as pure as I would have liked because there was also the <a href=\"https:\/\/www.betrisey.ch\/mini-foucault-n-22\">miniFoucault<\/a> oscillating at the same time in the same room and the three pendulums tested were barely adjusted. Why on earth not set them better before? Simply because it would have taken me a month per pendulum to do it properly and I don&#8217;t have three months to waste. Anyway, the experiment went like this.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">The experiment went like this, with a 15-second video capture taken automatically every hour for a fortnight:<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Test 1: pendulum 1 &amp; pendulum 3<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Test 2: pendulum 1 &amp; pendulum 2<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Test 3: pendulum 2 &amp; pendulum 3<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Pendulum 1 (left) weighs around 10 kg for a period of one second.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Pendulum 2 (centre) weighs about 3 kg for a period of 0.88 seconds.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Pendulum 3 (right) weighs about 6 kg for a period of one second.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">3 Raspberries, 1 Mac, a Siemens Logo as orchestra conductor. Behind the scenes: a real mess&#8230;<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"967\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/general-1024x967.jpg\" alt=\"\" class=\"wp-image-2984\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/general-1024x967.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/general-300x283.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/general-768x725.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/general-1536x1450.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/general-2048x1933.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n\n\n<figure class=\"wp-block-video\"><video height=\"720\" style=\"aspect-ratio: 1280 \/ 720;\" width=\"1280\" controls src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2023\/12\/synchros2.mp4\"><\/video><\/figure>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">The result was a bit of a cold war, with the planes of their rotations each moving as far away from the other as possible before stabilising their rotational speeds. So it was time for a real experiment, with two cameras taking photos. One of them took a photo at the end of each rotation of pendulum n\u00b03 and recorded the time of revolution on the digital clock. The other took a long exposure photo every hour, showing the direction of oscillation of each of the pendulums.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Experiment 2, from 31 December to 11 January. <\/strong><\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">3 January: launch of the 3 pendulums, all in the same direction.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">7 January: first results&#8230; Pendulum 2 is 30\u00b0 behind and pendulum 1 is 55\u00b0 behind. These differences have been stable for 2 days. The rotation time of the 3 pendulums is the same for all. <\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">8 January: production of an &#8220;angle trirapporteur&#8221; to show the different angles of oscillation of the 3 pendulums as a function of their rotation. It&#8217;s not exactly the kind of measuring instrument you&#8217;d find in a shop, but it&#8217;s very practical!<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"799\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/plexi-1024x799.jpg\" alt=\"\" class=\"wp-image-2992\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/plexi-1024x799.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/plexi-300x234.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/plexi-768x599.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/plexi-1536x1198.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/plexi-2048x1597.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Based on the following drawing:<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"522\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur2-1024x522.png\" alt=\"\" class=\"wp-image-2935\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur2-1024x522.png 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur2-300x153.png 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur2-768x391.png 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur2-1536x783.png 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur2-2048x1044.png 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">&#8230;and used in the following way. Sorry Apple, sorry so&#8230;<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"778\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur3-1024x778.jpg\" alt=\"\" class=\"wp-image-2945\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur3-1024x778.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur3-300x228.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur3-768x584.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur3-1536x1167.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/trirapporteur3-2048x1556.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" controls src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-2.mp4\"><\/video><\/figure>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Conclusions to 11 January 2024:<\/strong><\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Yes, the 3 clocks influence each other. They synchronise their rotations, shift a little and never leave their respective places. Two tiny but constant forces (Coriolis and a few tiny bends in a wall) interact, while other much larger forces such as the multiple air currents in my workshop have no effect. <\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">The times for each half-rotation were:<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">14.17 \/ 14.59 \/ 14.54 \/ 14.31 \/ 14.53 \/ 14.09 \/ 15.35 \/ 14.35 \/ 14.19 \/ 15.57 \/ 15.01 \/ 16.09 \/ 14.54<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Moral of the experiment: it&#8217;s not anarchy, love, dictatorship or the Cold War, but rather the story of an old couple who never meet.<\/strong><\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">Shift in the plane of rotation after 10 days: 61\u00b0 for pendulum n\u00b01 and 13\u00b0 for pendulum n\u00b02<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"630\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-2-1024x630.jpg\" alt=\"\" class=\"wp-image-2968\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-2-1024x630.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-2-300x184.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-2-768x472.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-2-1536x944.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-2-2048x1259.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Experiment 3: from 11 to 17 January, repetition of experiment 2 for confirmation<\/strong>. <\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">11 January: launch of the 3 pendulums, all in the same direction.<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">13 December: first results&#8230; Pendulum 2 is 14\u00b0 behind and pendulum 1 is 27\u00b0 behind. We are moving towards the same result as experiment 2.<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"527\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/decalage-1024x527.png\" alt=\"\" class=\"wp-image-2964\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/decalage-1024x527.png 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/decalage-300x154.png 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/decalage-768x395.png 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/decalage-1536x791.png 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/decalage.png 1729w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">15 December: Pendulum 2 lags 26\u00b0 and pendulum 1 lags 59\u00b0.<\/p>\n\n\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"768\" src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/image6-1024x768.jpg\" alt=\"\" class=\"wp-image-2971\" srcset=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/image6-1024x768.jpg 1024w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/image6-300x225.jpg 300w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/image6-768x576.jpg 768w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/image6-1536x1151.jpg 1536w, https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/image6-2048x1535.jpg 2048w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><\/figure>\n\n\n\n\n\n<figure class=\"wp-block-video\"><video height=\"1080\" style=\"aspect-ratio: 1920 \/ 1080;\" width=\"1920\" controls src=\"https:\/\/www.betrisey.ch\/wp-content\/uploads\/2024\/01\/test-3-synchro.mp4\"><\/video><\/figure>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">The times of each half-rotation were<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">14.33\/ 14.39 \/ 15.25 \/ 14.49 \/ 15.22 \/ 14.45 \/ 14.34 \/ 15.21 \/ 13.45<\/p>\n\n\n\n\n\n<p class=\"wp-block-paragraph\">The experiment was completed on 27 January and the measuring equipment dismantled to make way for the forthcoming Bravais pendulum.<\/p>\n\n","protected":false},"excerpt":{"rendered":"<p>Improbable experiment posted live&#8230;. The idea for this experiment came to me in 2002 in my studio when I saw two Foucault pendulums hanging from the same concrete ceiling, their rotations remaining perfectly synchronous for a whole month. They had been doing this for perhaps a year without me noticing. This couldn&#8217;t have happened by [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"footnotes":""},"class_list":["post-5154","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5154","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/comments?post=5154"}],"version-history":[{"count":1,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5154\/revisions"}],"predecessor-version":[{"id":5155,"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/pages\/5154\/revisions\/5155"}],"wp:attachment":[{"href":"https:\/\/www.betrisey.ch\/en\/wp-json\/wp\/v2\/media?parent=5154"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}