\n
\u4e00\u69d8\u91cd\u529b\u5834\u4e2d\u306e\u5358\u632f\u308a\u5b50<\/h3>\n
\u5358\u632f\u308a\u5b50\u306e\u3072\u3082\u306e\u9577\u3055\u3092 $\\ell$\uff0c\u91cd\u529b\u52a0\u901f\u5ea6\u306e\u5927\u304d\u3055\u3092 $g$\uff0c\u925b\u76f4\u4e0b\u5411\u304d\u304b\u3089\u306e\u632f\u308c\u89d2\u3092 $\\theta$ \u3068\u3059\u308b\u3068\uff0c\u5358\u632f\u308a\u5b50\u306e\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n
$$\\frac{d^2\\theta}{dt^2} = – \\frac{g}{\\ell} \\sin\\theta$$<\/p>\n
\u3068\u306a\u308b\u3002<\/p>\n
\u632f\u5e45\u304c\u5c0f\u3055\u3044\u5834\u5408\u306b\u306f\u5358\u632f\u52d5\u3068\u306a\u308b\u3053\u3068<\/h3>\n
$|\\theta| \\ll 1$ \u306e\u5834\u5408\u306b\u306f\uff0c$\\sin\\theta \\simeq \\theta$ \u3068\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u3067\uff0c\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n
$$\\frac{d^2\\theta}{dt^2} = – \\frac{g}{\\ell} \\theta$$<\/p>\n
\u3068\u306a\u308a\uff0c\u3053\u308c\u306f\u5358\u632f\u52d5\u3068\u306a\u308b\u3002\u5358\u632f\u52d5\u306e\u5468\u671f $\\tau_0$ \u306f<\/p>\n
$$\\tau_0 = 2 \\pi \\sqrt{\\frac{\\ell}{g}}$$<\/p>\n
\u3068\u306a\u308a\uff0c\u5358\u632f\u308a\u5b50\u306e\u3072\u3082\u306e\u9577\u3055\u3068\u91cd\u529b\u52a0\u901f\u5ea6\u3060\u3051\u3067\u6c7a\u307e\u308a\uff0c\u521d\u671f\u6761\u4ef6\u3067\u4e0e\u3048\u3089\u308c\u308b\u632f\u5e45 $\\theta_0$ \u306b\u4f9d\u5b58\u3057\u306a\u3044\u3002\u3053\u308c\u3092\u300c\u632f\u308a\u5b50\u306e\u7b49\u6642\u6027\u300d\u3068\u8a00\u3063\u305f\u308a\u3059\u308b\u3002<\/p>\n
\u7121\u6b21\u5143\u5316<\/h3>\n
\u5358\u632f\u52d5\u306e\u5468\u671f $\\tau_0$ \u3067\u7121\u6b21\u5143\u5316\u3057\u305f\u6642\u9593 $T$ \u3092<\/p>\n
$$T \\equiv \\frac{t}{\\tau_0}$$<\/p>\n
\u3068\u5b9a\u7fa9\u3059\u308b\u3002\u3053\u306e\u7121\u6b21\u5143\u5316\u3055\u308c\u305f\u6642\u9593\u5ea7\u6a19\u3067\u66f8\u3044\u305f\u904b\u52d5\u65b9\u7a0b\u5f0f\u306f<\/p>\n
$$\\frac{d^2 \\theta}{dT^2} = – 4 \\pi^2 \\sin\\theta$$<\/p>\n
\u3068\u306a\u308b\u3002<\/p>\n
\u554f\u984c\uff1a\u632f\u5e45\u304c\u5927\u304d\u3044\u5834\u5408\u306e\u5468\u671f\u306f\uff1f<\/h3>\n
\u632f\u5e45\u304c\u5927\u304d\u3044\uff0c\u3064\u307e\u308a $\\sin\\theta \\simeq \\theta$ \u3068\u8fd1\u4f3c\u3067\u304d\u306a\u3044\u5834\u5408\u306f\uff0c\u632f\u308a\u5b50\u306e\u5468\u671f\u306f\u4e00\u822c\u306b\u632f\u5e45\u306b\u4f9d\u5b58\u3059\u308b\u306e\u3067\u306f\u306a\u3044\u304b\u3068\u8003\u3048\u3089\u308c\u308b\u3002<\/p>\n
\u305d\u3053\u3067\uff0c$T = 0$ \u3067\u306e\u632f\u5e45 $\\theta_0$ \u3092\u305f\u3068\u3048\u3070 10\u00b0 \u304b\u3089 90\u00b0 \u307e\u3067 10\u00b0 \u304d\u3056\u307f\u3067\u5927\u304d\u304f\u3057\u3066\u3044\u3063\u305f\u5834\u5408\uff0c\u3075\u308a\u3053\u306e\u5468\u671f\u306f\u3069\u3046\u306a\u308b\u304b\uff1f\u3000\u3068\u3044\u3046\u306e\u304c\u554f\u984c\u3002<\/p>\n
\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u3067\u89e3\u304f\u305f\u3081\u306e\u6e96\u5099<\/h3>\n
2\u968e\u5e38\u5fae\u5206\u65b9\u7a0b\u5f0f\u3092\u30eb\u30f3\u30b2\u30fb\u30af\u30c3\u30bf\u6cd5\u3067\u6570\u5024\u7684\u306b\u89e3\u304f\u305f\u3081\u306b\u306f\uff0c\u9023\u7acb1\u968e\u5fae\u5206\u65b9\u7a0b\u5f0f\u7cfb\u306b\u306a\u304a\u3059\u3002<\/p>\n
\\begin{eqnarray}
\n\\frac{d\\theta}{dT} &=& F_1(V) = V \\\\
\n\\frac{dV}{dT} &=& F_2(\\theta) = – 4 \\pi^2 \\sin\\theta
\n\\end{eqnarray}<\/p>\n
\u3053\u308c\u3092\u521d\u671f\u6761\u4ef6 $T = 0$ \u3067<\/p>\n
\\begin{eqnarray}
\n\\theta(0) &=& \\theta_0 \\\\
\nV(0) &=& 0
\n\\end{eqnarray}<\/p>\n
\u3068\u3057\uff0c$\\theta_0 = 10^{\\circ}, \\ 60^{\\circ}, \\ 80^{\\circ}$ \u306e\u5834\u5408\u306b $T_0 = 0$ \u304b\u3089 $ T_1 = 2$ \u307e\u3067\u89e3\u304f\u3002<\/p>\n
\uff08\u304f\u3069\u3044\u3088\u3046\u3067\u3059\u304c\uff0c\u898f\u683c\u5316\u3055\u308c\u305f\u6642\u9593\u3067 $T_1 = 2$ \u3068\u3044\u3046\u306e\u306f\uff0c\u5358\u632f\u52d5\u306e\u5834\u5408\u306e\u5468\u671f $\\tau_0$ \u306e 2 \u500d\u306e\u6642\u9593\u307e\u3067\uff0c\u3068\u3044\u3046\u610f\u5473\u3067\u3059\u3088\u3002\uff09<\/p>\n<\/div>\n<\/div>\n<\/div>\n