{"id":378,"date":"2026-01-26T16:44:43","date_gmt":"2026-01-26T16:44:43","guid":{"rendered":"https:\/\/www.jeffnathanson.com\/NateHart\/?page_id=378"},"modified":"2026-01-26T16:44:43","modified_gmt":"2026-01-26T16:44:43","slug":"instabilities-in-flexible-helices","status":"publish","type":"page","link":"https:\/\/www.jeffnathanson.com\/NateHart\/instabilities-in-flexible-helices\/","title":{"rendered":"Instabilities in Flexible Helices"},"content":{"rendered":"\n<p>My sophomore year, I worked with Professor Andy Borum studying instabilities in flexible helices. We observe the behavior of a typical desktop Slinky toy. By holding the ends at certain angles and separating them, we can observe a snapping instability where the Slinky quickly shifts between equilibria positions. Using Professor Borum&#8217;s Slinky model, I performed numerical simulations with the goal of recreating this experimentally observed bifurcation. As this work has not yet been published, I&#8217;ll refrain from giving the entire mathematical model for the slinky, but I will present the following plot.<\/p>\n\n\n\n<figure class=\"wp-block-image size-large\"><img loading=\"lazy\" decoding=\"async\" width=\"1024\" height=\"444\" src=\"https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-1024x444.png\" alt=\"\" class=\"wp-image-379\" srcset=\"https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-1024x444.png 1024w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-300x130.png 300w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-768x333.png 768w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-1536x666.png 1536w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-2048x888.png 2048w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-1200x520.png 1200w, https:\/\/www.jeffnathanson.com\/NateHart\/wp-content\/uploads\/2026\/01\/Exp_Plot-1980x858.png 1980w\" sizes=\"auto, (max-width: 1024px) 100vw, 1024px\" \/><figcaption class=\"wp-element-caption\">The vertical axis represents the height of the middle of the slinky and the horizontal axis represents the separation of the slinky. The solid curves show the equilibria positions predicted by the numerical model and the data points are from empirical data. We see qualitative agreement for each angle of where there is and isn&#8217;t the snapping instability.<\/figcaption><\/figure>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>My sophomore year, I worked with Professor Andy Borum studying instabilities in flexible helices. We observe the behavior of a typical desktop Slinky toy. By holding the ends at certain angles and separating them, we can observe a snapping instability where the Slinky quickly shifts between equilibria positions. Using Professor Borum&#8217;s Slinky model, I performed [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-378","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages\/378","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/comments?post=378"}],"version-history":[{"count":1,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages\/378\/revisions"}],"predecessor-version":[{"id":380,"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/pages\/378\/revisions\/380"}],"wp:attachment":[{"href":"https:\/\/www.jeffnathanson.com\/NateHart\/wp-json\/wp\/v2\/media?parent=378"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}