{"id":5790,"date":"2025-03-03T12:24:22","date_gmt":"2025-03-03T03:24:22","guid":{"rendered":"https:\/\/torisetudy.com\/?p=5790"},"modified":"2025-03-03T12:24:25","modified_gmt":"2025-03-03T03:24:25","slug":"y-t%e3%82%b0%e3%83%a9%e3%83%95%e3%81%ae%e6%95%b0%e5%bc%8f%e8%a1%a8%e7%8f%be","status":"publish","type":"post","link":"https:\/\/torisetudy.com\/?p=5790","title":{"rendered":"y-t\u30b0\u30e9\u30d5\u306e\u6570\u5f0f\u8868\u73fe"},"content":{"rendered":"\n<p><\/p>\n\n\n\n<div id=\"toc_container\" class=\"no_bullets\"><p class=\"toc_title\">\u76ee\u6b21<\/p><ul class=\"toc_list\"><li><a href=\"#y-t\"><span class=\"toc_number toc_depth_1\">1<\/span> $y-t$ \u30b0\u30e9\u30d5\u306e\u6570\u5f0f\u8868\u8a18<\/a><\/li><li><a href=\"#i\"><span class=\"toc_number toc_depth_1\">2<\/span> \u4e00\u822c\u5316<\/a><\/li><\/ul><\/div>\n<h2 class=\"wp-block-heading\"><span id=\"y-t\">$y-t$ \u30b0\u30e9\u30d5\u306e\u6570\u5f0f\u8868\u8a18<\/span><\/h2>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon1 clearfix\"><div class=\"st-kaiwa-face\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name\">\u7fbd\u767d<\/div><\/div><div class=\"st-kaiwa-area\"><div class=\"st-kaiwa-hukidashi\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>\u4eca\u56de\u306f $y-t$ \u30b0\u30e9\u30d5\u3092\u6570\u5f0f\u5316\u3057\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n<\/div><\/div><\/div><\/div>\n\n\n\n<p>$x=0$ \u306e\u5a92\u8cea\u306e $y-t$ \u30b0\u30e9\u30d5\u304c\u6b21\u56f3\u306e\u3068\u304a\u308a\u3067\u3042\u3063\u305f\u3068\u304d\u3001\u3053\u306e\u5a92\u8cea\u306e\u5909\u4f4d\u3092\u8868\u3059\u5f0f $y(0,\\,t)$ \u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n<figure class=\"wp-block-image size-large physicsimg\"><img decoding=\"async\" width=\"177\" height=\"125\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/\u7269\u7406654.svg\" alt=\"\" class=\"wp-image-5808\"\/><noscript><img decoding=\"async\" width=\"177\" height=\"125\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/\u7269\u7406654.svg\" alt=\"\" class=\"wp-image-5808\"\/><\/noscript><\/figure>\n\n\n\n<p>\u305d\u3046\u306f\u3044\u3063\u3066\u3082\u3001\u307e\u305f\u30a4\u30c1\u304b\u3089\u8003\u3048\u308b\u5fc5\u8981\u306f\u3042\u308a\u307e\u305b\u3093\u3002$y-x$ \u30b0\u30e9\u30d5\u306b\u3064\u3044\u3066\u5b66\u3093\u3060\u5185\u5bb9\u304c\u305d\u306e\u307e\u307e\u5229\u7528\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u4eca\u56de\u3082\u4e0e\u3048\u3089\u308c\u3066\u3044\u308b\u30b0\u30e9\u30d5\u3082 $+\\sin$ \u578b\u3067\u3042\u308a\u3001$x\\to t$\u3001$\\lambda\\to T$ \u3068\u3044\u3046\u5bfe\u5fdc\u95a2\u4fc2\u304c\u3042\u308b\u3053\u3068\u304c\u308f\u304b\u308a\u307e\u3059\u306d\u3002\u3088\u3063\u3066\u3001$y-x$ \u30b0\u30e9\u30d5\u3092\u8868\u3059\u3068\u304d\u306b\u6c42\u3081\u305f<\/p>\n\n\n\n<p>$$y(x,\\,0)=A\\sin2\\pi\\bun{x}{\\lambda}$$\u3068\u3044\u3046\u6570\u5f0f\u4e0a\u306b\u304a\u3044\u3066\u3082 $x\\to t$\u3001$\\lambda\\to T$ \u3068\u66f8\u304d\u63db\u3048\u308c\u3070\u3088\u304f\u3001<\/p>\n\n\n\n<p>$$y(0,\\,t)=A\\sin2\\pi\\bun{t}{T}$$\u3068\u3057\u3066\u3059\u3050\u306b\u7d50\u8ad6\u304c\u5f97\u3089\u308c\u307e\u3059\u3002<\/p>\n\n\n\n<div style=\"height:10px\" aria-hidden=\"true\" class=\"wp-block-spacer\"><\/div>\n\n\n\n<p>\u3084\u306f\u308a $t$ \u304c $T$\uff081\u5468\u671f\u5206\uff09\u5897\u3048\u308b\u3054\u3068\u306b\u3001\u4f4d\u76f8\u306f $2\\pi$ \u5897\u3048\u308b\u3053\u3068\u304c\u78ba\u8a8d\u3067\u304d\u307e\u3059\u306d\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">\u6570\u5f0f\u306e\u89e3\u91c8<\/h3>\n\n\n\n<p>\u3055\u3066\u3001\u3053\u3053\u3067\u51fa\u3066\u304d\u305f $\\Bun{t}{T}$ \u3068\u3044\u3046\u5024\u306b\u3082\u91cd\u8981\u306a\u610f\u5473\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n<p>$t$ \u3092\u6642\u9593\u306e\u5468\u671f $T$ \u3067\u5272\u3063\u305f\u5024\u3067\u3042\u308b $\\Bun{t}{T}$ \u306f\u3001\u300c\u6642\u9593 $t$ \u306e\u30ba\u30ec\u304c\u3001\u6ce2\u4f55\u500b\u5206\u306e\u6642\u9593\u306e\u30ba\u30ec\u306b\u76f8\u5f53\u3059\u308b\u304b\u300d\u3092\u8868\u3059\u5024\u3067\u3059\u3002\u305d\u3057\u3066\u3053\u308c\u306b\u4f4d\u76f8\u306e\u5468\u671f $2\\pi$ \u3092\u304b\u3051\u305f\u5024\u3067\u3042\u308b $2\\pi\\Bun{t}{T}$ \u306f\u3001\u300c\u6642\u9593\u306e\u305a\u308c $t$ \u306b\u5bfe\u5fdc\u3059\u308b\u4f4d\u76f8\u306e\u30ba\u30ec\u300d\u3068\u8003\u3048\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n<p>\u300c\u6642\u9593\u304c $t$ \u3060\u3051\u305a\u308c\u308b\u3068\u3001\u4e09\u89d2\u95a2\u6570\u306e\u4e2d\u8eab\u306f $2\\pi\\Bun{t}{T}$ \u3060\u3051\u305a\u308c\u308b\u3088\uff01\u300d\u3068\u3044\u3046\u3053\u3068\u3067\u3059\u3002<\/p>\n\n\n\n<div class=\"st-kaiwa-box kaiwaicon1 clearfix\"><div class=\"st-kaiwa-face\"><img decoding=\"async\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><noscript><img decoding=\"async\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/2022\/07\/\u5b8c\u6210\u30a2\u30a4\u30b3\u30f3.png\" width=\"60px\"><\/noscript><div class=\"st-kaiwa-face-name\">\u7fbd\u767d<\/div><\/div><div class=\"st-kaiwa-area\"><div class=\"st-kaiwa-hukidashi\"><div class=\"wp-block-st-blocks-st-kaiwa\">\n<p>$2\\pi\\Bun{x}{\\lambda}$ \u306e\u8003\u3048\u65b9\u3068\u540c\u69d8\u3067\u3059\u306d\u3002<\/p>\n<\/div><\/div><\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-large physicsimg\"><img decoding=\"async\" width=\"361\" height=\"122\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/\u7269\u7406655.svg\" alt=\"\" class=\"wp-image-5809\"\/><noscript><img decoding=\"async\" width=\"361\" height=\"122\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/\u7269\u7406655.svg\" alt=\"\" class=\"wp-image-5809\"\/><\/noscript><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><span id=\"i\">\u4e00\u822c\u5316<\/span><\/h2>\n\n\n\n<p>$y-t$ \u30b0\u30e9\u30d5\u3082\u4e00\u822c\u5316\u3057\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002$y-x$ \u30b0\u30e9\u30d5\u306e\u5834\u5408\u3068\u540c\u69d8\u306b\u8003\u3048\u308b\u3068\u3001<\/p>\n\n\n\n<p>$$y(x,\\,0)=A\\sin\\left(2\\pi\\bun{t}{T}+\\varphi\\right)$$\u3067 OK \u3067\u3059\u306d\u3002<\/p>\n\n\n\n<div class=\"wp-block-st-blocks-my-box st-mybox has-title post-hashiro-point\" style=\"background-color:#fff;border-color:#ff7f50\"><p class=\"st-mybox-title\" style=\"color:#ff7f50;font-weight:bold;text-shadow:#fff 3px 0px 0px, #fff 2.83487px .981584px 0px, #fff 2.35766px 1.85511px 0px, #fff 1.62091px 2.52441px 0px, #fff .705713px 2.91581px 0px, #fff -0.287171px 2.98622px 0px, #fff -1.24844px 2.72789px 0px, #fff -2.07227px 2.16926px 0px, #fff -2.66798px 1.37182px 0px, #fff -2.96998px .42336px 0px, #fff -2.94502px -0.571704px 0px, #fff -2.59586px -1.50383px 0px, #fff -1.96093px -2.27041px 0px, #fff -1.11013px -2.78704px 0px, #fff -0.137119px -2.99686px 0px, #fff .850987px -2.87677px 0px, #fff 1.74541px -2.43999px 0px, #fff 2.44769px -1.73459px 0px, #fff 2.88051px -0.838246px 0px;background:linear-gradient(0deg, #fff 0%, #fff 55%, rgba(0, 0, 0, 0) 55%, rgba(0, 0, 0, 0) 100%)\"><i class=\"st-fa st-svg-lightbulb-o st-css-no\" aria-hidden=\"\"><\/i>$y-t$\u30b0\u30e9\u30d5\u306e\u6570\u5f0f\u8868\u73fe<\/p><div class=\"st-in-mybox\">\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">\u632f\u5e45\u304c $A$\uff0c\u5468\u671f\u304c $T$ \u3067\u3042\u308b\u6b63\u5f26\u9032\u884c\u6ce2\u306b\u304a\u3044\u3066\uff0c$x=0$ \u306e\u4f4d\u7f6e\u306e\u5a92\u8cea\u306e\uff0c\u6642\u523b$t$ \u306b\u304a\u3051\u308b\u5909\u4f4d $y(0,\\,t)$ \u306f\u3001<\/p>\n\n\n\n<p class=\"has-st-margin-bottom has-st-margin-bottom--1\">$$y(0,\\,t)=A\\sin\\left(2\\pi\\bun{t}{T}+\\varphi\\right)$$\u306e\u5f62\u3067\u8868\u3055\u308c\u308b\u3002\u3053\u306e\u6570\u5f0f\u3092\u30b0\u30e9\u30d5\u3068\u3057\u3066\u53ef\u8996\u5316\u3057\u305f\u3082\u306e\u304c $y-t$\u30b0\u30e9\u30d5\u3067\u3042\u308b\u3002<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-st-blocks-midashi-box freebox has-title post-hashiro-reidai\" style=\"background-color:#f7f7fb;border-width:3px;border-color:#a3bded\"><p class=\"p-free\" style=\"border-color:#a3bded;font-weight:bold\"><span class=\"p-entry-f\" style=\"color:#ffffff;font-weight:bold;background-color:#a3bded\"><i class=\"st-fa st-svg-pencil st-css-no\" aria-hidden=\"\"><\/i>\u4f8b\u984c<\/span><\/p><div class=\"free-inbox\">\n<p>\u539f\u70b9\u306e\u5a92\u8cea\u306e\uff0c\u6642\u523b$t\\s$ \u306b\u304a\u3051\u308b\u5909\u4f4d$y\\m$ \u304c\uff0c$y(0,\\,t)=-4.0\\sin\\bun{\\pi t}{3.0}\\m$ \u3067\u8868\u3055\u308c\u308b\u3068\u304d\uff0c\u3053\u306e\u5a92\u8cea\u306e\u632f\u52d5\u306e\u69d8\u5b50\u3092\u8868\u3059 $y-t$\u30b0\u30e9\u30d5\u306e\u6982\u5f62\u3092\u304b\u3051\u3002<\/p>\n<\/div><\/div>\n\n\n\n<div class=\"wp-block-group post-hashiro-reidaikaitou\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<div class=\"wp-block-group\"><div class=\"wp-block-group__inner-container is-layout-constrained wp-block-group-is-layout-constrained\">\n<p>\u4e0e\u3048\u3089\u308c\u305f\u5909\u4f4d\u306e\u5f0f\u306f\u3001<\/p>\n\n\n\n<p>$$y(0,\\,t)=-4.0\\sin2\\pi\\bun{t}{6.0}\\m$$\u3068\u5909\u5f62\u3067\u304d\u308b\u3002<\/p>\n\n\n\n<p>\u3088\u3063\u3066\uff0c\u632f\u5e45\u306f $4.0\\m$\uff0c\u5468\u671f\u306f $6.0\\s$ \u3067\u3042\u308a\uff0c\u30b0\u30e9\u30d5\u304c $-\\sin$\u578b\u3068\u306a\u308b\u3053\u3068\u306b\u6ce8\u610f\u3059\u308b\u3068\uff0c\u6b21\u56f3\u306e\u901a\u308a\u3002<\/p>\n<\/div><\/div>\n\n\n\n<figure class=\"wp-block-image size-large physicsimg\"><img decoding=\"async\" width=\"188\" height=\"129\" src=\"data:image\/gif;base64,R0lGODlhAQABAAAAACH5BAEKAAEALAAAAAABAAEAAAICTAEAOw==\" data-src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/\u7269\u7406660.svg\" alt=\"\" class=\"wp-image-5814\"\/><noscript><img decoding=\"async\" width=\"188\" height=\"129\" src=\"https:\/\/torisetudy.com\/wp-content\/uploads\/\u7269\u7406660.svg\" alt=\"\" class=\"wp-image-5814\"\/><\/noscript><\/figure>\n<\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u76ee\u6b211 $y-t$ \u30b0\u30e9\u30d5\u306e\u6570\u5f0f\u8868\u8a182 \u4e00\u822c\u5316 $y-t$ \u30b0\u30e9\u30d5\u306e\u6570\u5f0f\u8868\u8a18 $x=0$ \u306e\u5a92\u8cea\u306e $y-t$ \u30b0\u30e9\u30d5\u304c\u6b21\u56f3\u306e\u3068\u304a\u308a\u3067\u3042\u3063\u305f\u3068\u304d\u3001\u3053\u306e\u5a92\u8cea\u306e\u5909\u4f4d\u3092\u8868\u3059\u5f0f $y(0,\\,t)$ \u3092\u6c42\u3081\u3066 &#8230; <\/p>\n","protected":false},"author":1,"featured_media":5634,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,39],"tags":[],"class_list":["post-5790","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-wave","category-39"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5790"}],"collection":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5790"}],"version-history":[{"count":34,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5790\/revisions"}],"predecessor-version":[{"id":5978,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/posts\/5790\/revisions\/5978"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=\/wp\/v2\/media\/5634"}],"wp:attachment":[{"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5790"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5790"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/torisetudy.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5790"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}