{"id":2561,"date":"2012-07-11T19:09:47","date_gmt":"2012-07-12T01:09:47","guid":{"rendered":"http:\/\/www.contrapositivediary.com\/?p=2561"},"modified":"2012-07-11T19:13:00","modified_gmt":"2012-07-12T01:13:00","slug":"kids-as-parametric-oscillators","status":"publish","type":"post","link":"https:\/\/www.contrapositivediary.com\/?p=2561","title":{"rendered":"Kids as Parametric Oscillators"},"content":{"rendered":"<p>Back in June, when Carol and I were in Chicago, we took our nieces to the school playground across the big field behind my sister&#8217;s house. We pushed them on the swings, as usual, and I considered that both girls are tall and muscular for their ages. So I asked, &#8220;Katie, do you know how to pump?&#8221;<\/p>\n<p>&#8220;What&#8217;s pump?&#8221;<\/p>\n<p>&#8220;It&#8217;s pushing yourself on a swing so nobody else has to push you!&#8221;<\/p>\n<p>She looked at me funny. She does that a lot; it&#8217;s part of the Uncle Jeff job description. So while pushing her I prepared to answer the obvious question: <em>How do I do that, Uncle Jeff?<\/em><\/p>\n<p>I stood there for a second before I realized that I had not pumped a swing for, well, <em>decades<\/em>. I wasn&#8217;t entirely sure I remembered how to do it. I gave Katie an extra big push and jumped onto the swing next to hers.<\/p>\n<p>Shazam! The mind may forget&#8230;the body remembers! In thirty seconds I was going <em>way<\/em> high, and was devising my tutorial for the scarily bright little girl three feet to my left:<\/p>\n<blockquote>\n<p><em><em>As you go forward, pull back on the chains and stretch your feet out. When you start to go back, stop pulling on the chains and pull your feet underneath you.<\/em><\/em><\/p>\n<\/blockquote>\n<p>Wait a minute. Wait one damned minute! <em>How does that work?<\/em> I mean, I&#8217;m not pushing against the ground or anything else, and not hurling reaction mass. I realized that while the body remembered clearly how to pump a swing, the mind could not explain it.<\/p>\n<p>I vaguely and anciently recalled reading something about a swing with a kid on it acting as a parametric oscillator, but the details were just gone. My guess at the time was a good one: When you pump a swing, you&#8217;re raising and lowering your center of mass a little by &#8220;bending&#8221; the pendulum, synchronized to the timing of the swing&#8217;s motion. That adds energy during the forward motion of the swing. There are explanations all over the Web, but <a href=\"http:\/\/www.grinnell.edu\/academic\/physics\/faculty\/case\/swing\/\" target=\"_blank\">the one I found by Dr. William Case at Grinnell College<\/a> was the best, including several short video clips.<\/p>\n<p>It&#8217;s an amazingly subtle business.<\/p>\n<p>I&#8217;m kicking myself now for not thinking to try the obvious enhancement, which is pushing forward on the chains at the rear extreme of motion. Next time.<\/p>\n<p>Katie didn&#8217;t quite get it but she gave it a good shot (heck, I was at least six before my cousin Diane taught me circa 1958) and with a little practice she&#8217;ll remember it well past her sixtieth birthday in 2066, and possibly even into the 22nd Century.<\/p>\n<p>Some things are just timeless.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Back in June, when Carol and I were in Chicago, we took our nieces to the school playground across the big field behind my sister&#8217;s house. We pushed them on the swings, as usual, and I considered that both girls are tall and muscular for their ages. So I asked, &#8220;Katie, do you know how [&hellip;]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[23],"tags":[47,54],"class_list":["post-2561","post","type-post","status-publish","format-standard","hentry","category-ideasandanalysis","tag-family","tag-science"],"_links":{"self":[{"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=\/wp\/v2\/posts\/2561","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2561"}],"version-history":[{"count":3,"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=\/wp\/v2\/posts\/2561\/revisions"}],"predecessor-version":[{"id":2564,"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=\/wp\/v2\/posts\/2561\/revisions\/2564"}],"wp:attachment":[{"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2561"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2561"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.contrapositivediary.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2561"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}