{"id":36727,"date":"2025-05-12T11:35:36","date_gmt":"2025-05-12T03:35:36","guid":{"rendered":"http:\/\/www.qiusir.com\/?p=36727"},"modified":"2025-05-12T11:35:36","modified_gmt":"2025-05-12T03:35:36","slug":"%e4%ba%8c%e4%bd%93%e9%97%ae%e9%a2%98%e4%b8%8e%e7%ba%a6%e5%8c%96%e8%b4%a8%e9%87%8f","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=36727","title":{"rendered":"\u4e8c\u4f53\u95ee\u9898\u4e0e\u7ea6\u5316\u8d28\u91cf"},"content":{"rendered":"

JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c6\u671f\uff082025.4.29\uff09
\n\"\"
\n

\u4e8c\u4f53\u95ee\u9898\u4e0e\u7ea6\u5316\u8d28\u91cf<\/strong>
\n\"\"
\nJQX|Xiao
\n<\/center><\/p>\n

\u4e00\u3001\u6c34\u5e73\u5f39\u7c27\u53cc\u7403\u7cfb\u7edf\u7684\u7b80\u8c10\u632f\u52a8\u5206\u6790
\n\u6c34\u5e73\u9762\u4e0a\u6709\u4e24\u4e2a\u8d28\u91cf\u5206\u522b\u4e3a$$m_1$$\u548c$$m_2$$\u7684\u4e24\u4e2a\u5c0f\u7403\uff0c\u4e2d\u95f4\u7531\u4e00\u4e2a\u52b2\u5ea6\u7cfb\u6570\u4e3ak\u7684\u5f39\u7c27\u8fde\u63a5\u3002\u6211\u4eec\u5206\u6790\u8be5\u7cfb\u7edf\u505a\u7b80\u8c10\u632f\u52a8\u7684\u6027\u8d28\u3002
\n\"\"
\n1.\u6c42\u5468\u671f\uff1a\u7531\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\uff0c\u4e24\u4e2a\u5c0f\u7403\u7684\u8fd0\u52a8\u65b9\u7a0b\u662f\uff1a$$m_1 \\ddot{r}_1 = k(r – r_0) $$,
\n$$m_2 \\ddot{r}_2 = -k(r – r_0)$$\uff0c\u5c06\u4e24\u4e2a\u65b9\u7a0b\u8054\u7acb\u53ef\u5f97\uff1a$$\\ddot{r}_2 – \\ddot{r}_1 = \\ddot{r} = -k \\left( \\frac{1}{m_1} + \\frac{1}{m_2} \\right) (r – r_0)$$\uff0c\u5316\u7b80\u4e3a\uff1a$$\\ddot{r} = -\\frac{k}{\\mu}(r – r_0)$$\u3002\u5f15\u5165\u7ea6\u5316\u8d28\u91cf\uff1a$$\\mu = \\frac{m_1 m_2}{m_1 + m_2}$$\uff0c\u53ef\u4ee5\u770b\u5230\u632f\u52a8\u65b9\u7a0b\u6709\u7b80\u8c10\u632f\u52a8\u7684\u5f62\u5f0f\uff0c\u632f\u52a8\u7684\u9891\u7387\u4e3a\uff1a$$\\omega = \\sqrt{\\frac{k}{\\mu}}$$\uff0c\u6839\u636e\u5468\u671f\u516c\u5f0f\uff1a$$T = \\frac{2\\pi}{\\omega} = 2\\pi \\sqrt{\\frac{\\mu}{k}} = 2\\pi \\sqrt{ \\frac{m_1 m_2}{(m_1 + m_2) k} }$$\u3002\u8be5\u7cfb\u7edf\u53ef\u7b49\u6548\u4e3a\u8d28\u91cf\u4e3a$$ \\mu$$\u7684\u5355\u8d28\u70b9\u5728\u5f39\u7c27\u529b\u4f5c\u7528\u4e0b\u7684\u7b80\u8c10\u8fd0\u52a8\u3002<\/p>\n

2.\u4e24\u4e2a\u5c0f\u7403\u7684\u632f\u5e45\uff1a\u6839\u636e\u80fd\u91cf\u5b88\u6052\u5b9a\u5f8b\uff1a$$\\frac{1}{2} \\mu v_0^2 = \\frac{1}{2} k A^2$$\uff0c\u53ef\u5f97\uff1a$$A = v_0 \\sqrt{\\frac{\\mu}{k}} = v_0 \\sqrt{ \\frac{m_1 m_2}{(m_1 + m_2) k} }$$\uff0c\u4e24\u4e2a\u5c0f\u7403\u7684\u632f\u5e45\u6309\u7167\u8d28\u91cf\u5206\u914d\uff0c$$A_1 = A \\cdot \\frac{m_2}{m_1 + m_2} ,A_2 = A \\cdot \\frac{m_1}{m_1 + m_2}$$ \u3002
\n\u6c42\u4efb\u610f\u65f6\u523b\u4e24\u4e2a\u5c0f\u7403\u7684\u4f4d\u7f6e\u5750\u6807\uff1a\u4ee5\u8d28\u5fc3\u4e3a\u53c2\u8003\u7cfb\uff1a\u4e24\u4e2a\u5c0f\u7403\u5206\u522b\u505a\u7b80\u8c10\u632f\u52a8\uff0c\u6839\u636e\u52a8\u91cf\u5b88\u8861\u5b9a\u5f8b\uff0c\u901f\u5ea6\u548c\u76f8\u5bf9\u8d28\u5fc3\u4f4d\u79fb\u6309\u7167\u8d28\u91cf\u7684\u53cd\u6bd4\u5206\u914d\uff0c\u5750\u6807\u5206\u522b\u4e3a$$A_1 = A \\cdot \\frac{m_2}{m_1 + m_2} ,A_2 = A \\cdot \\frac{m_1}{m_1 + m_2}$$ \u3002
\n3.\u4e24\u4e2a\u5c0f\u7403\u7684\u4f4d\u7f6e\u5750\u6807\uff1a\u56de\u5230\u5730\u9762\u7cfb\uff0c\u8d28\u5fc3\u901f\u5ea6\u4e3a$$V_c = \\frac{m_1}{m_1 + m_2} V_0$$\uff0c\u4e3a\u7b80\u5316\u8fd0\u7b97\uff0c\u4ee5\u521d\u59cb\u65f6\u523b\u8d28\u5fc3\u5750\u6807\u4e3a\u5750\u6807\u539f\u70b9\uff0c\u8d28\u5fc3\u4f4d\u79fb\u4e3a$$x_c(t) = v_c t=\\frac{m_1}{m_1 + m_2} V_0 t$$\u3002\u4e24\u4e2a\u5c0f\u7403\u5728\u5730\u9762\u53c2\u8003\u7cfb\u4e0b\u7684\u4f4d\u7f6e\u5750\u6807\u4e3a\uff1a$$x_1(t) = x_c(t) – A \\cdot \\frac{m_2}{m_1 + m_2} \\sin(\\omega t)$$ ,
\n$$x_2(t) = x_c(t) + A \\cdot \\frac{m_1}{m_1 + m_2} \\sin(\\omega t)$$\u3002\u9644\uff1a\u82e5\u4e24\u4e2a\u5c0f\u7403\u8d28\u91cf\u76f8\u7b49\uff0c\u4f1a\u51fa\u73b0\u5f88\u6709\u8da3\u7684\u7ed3\u679c\uff0c\u5728\u5730\u9762\u53c2\u8003\u7cfb\u4e0b\uff0c\u4e24\u4e2a\u5c0f\u7403\u76f8\u5dee$$\\pi$$\u4e2a\u76f8\u4f4d\uff0c\u5e73\u5747\u800c\u8a00\uff0c\u4e24\u4e2a\u5c0f\u7403\u5728\u63a8\u548c\u62c9\u7684\u8fc7\u7a0b\u6574\u4f53\u5411\u53f3\u8fd0\u52a8\uff0c\u4f46\u662f\u5b83\u4eec\u5c06\u4ea4\u66ff\u8fbe\u5230\u9759\u6b62\uff0c\u4e00\u4e2a\u901f\u5ea6\u6700\u5927\u65f6\uff0c\u53e6\u4e00\u4e2a\u901f\u5ea6\u4e3a\u96f6\u3002
\n\"\"<\/p>\n

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\n\u5c06\u4e24\u4e2a\u5c0f\u7403\u4e0e\u5f39\u7c27\u7ec4\u6210\u7684\u7cfb\u7edf\u7528\u7ec6\u7ebf\u7ad6\u76f4\u60ac\u6302\uff0c\u5e76\u5904\u4e8e\u9759\u6b62\u72b6\u6001\u3002\u73b0\u5c06\u7ec6\u7ebf\u70e7\u65ad\uff0c\u8bd5\u5206\u6790\u4e24\u4e2a\u5c0f\u7403\u7684\u8fd0\u52a8\uff1f\u540c\u6c34\u5e73\u65b9\u5411\uff0c\u4e24\u4e2a\u5c0f\u7403\u7684\u725b\u4e8c\u5b9a\u5f8b\u540c\u6837\u6ee1\u8db3\u7b80\u8c10\u632f\u52a8\u7684\u8d28\u70b9\u8fd0\u52a8\u65b9\u7a0b\uff0c\u56e0\u6b64\u5728\u8d28\u5fc3\u7cfb\u4e24\u4e2a\u5c0f\u7403\u5c06\u540c\u6837\u505a\u7b80\u8c10\u632f\u52a8\uff0c\u5176\u632f\u5e45\u548c\u5468\u671f\u7684\u5206\u6790\u65b9\u6cd5\u4e0e\u6c34\u5e73\u65b9\u5411\u7684\u60c5\u5f62\u76f8\u540c\uff0c\u7ed3\u8bba\u4e00\u81f4\u3002\u4f46\u662f\u5728\u5730\u9762\u53c2\u8003\u7cfb\u4e2d\uff0c\u8d28\u5fc3\u5728\u505a\u81ea\u7531\u843d\u4f53\u8fd0\u52a8\uff0c\u8fd0\u52a8\u65b9\u7a0b\u4f1a\u7a0d\u6709\u4e0d\u540c\uff0c\u8fd9\u91cc\u4e0d\u505a\u8be6\u7ec6\u63a8\u5bfc\u3002<\/p>\n

\u4e09\u3001\u53cc\u661f\u95ee\u9898
\n\u4e24\u4e2a\u8d28\u91cf\u5206\u522b\u4e3a$$m_1,m_2$$\u7684\u4e24\u4e2a\u5929\u4f53\uff0c\u8ddd\u79bb\u4e3ar\uff0c\u5f15\u529b\u5927\u5c0f\u4e3a$$F = \\frac{G m_1 m_2}{r^2}$$\uff0c\u6839\u636e\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\uff0c\u5bf9\u4e24\u4e2a\u7269\u4f53\u5206\u522b\u6709$$F = m_1 a_1,F = -m_2 a_2 $$\u3002\u4e24\u4e2a\u661f\u4f53\u7684\u76f8\u5bf9\u52a0\u901f\u5ea6\u4e3a$$a = a_1 – a_2 = \\left( \\frac{1}{m_1} + \\frac{1}{m_2} \\right) F$$ \uff0c\u5f15\u5165\u7ea6\u5316\u8d28\u91cf$$\\mu$$,\u6839\u636e\u5411\u5fc3\u529b\u516c\u5f0f\u548c\u725b\u987f\u7b2c\u4e8c\u5b9a\u5f8b\uff1a$$\\mu \\omega^2 r = \\frac{G m_1 m_2}{r^2}$$ ,\u89e3\u5f97\u5468\u671fT\u4e3a\uff1a$$T = \\frac{2\\pi}{\\omega} = 2\\pi \\sqrt{ \\frac{r^3}{G(m_1 + m_2)} }$$\u3002\u4e0e\u6211\u4eec\u5e38\u89c4\u63a8\u5bfc\u65b9\u6cd5\u76f8\u540c\u3002<\/p>\n

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\n\u4ece$$T=2\\pi\\sqrt{\\frac{R}{g}}$$\u7684\u7406\u89e3\u5165\u624b\uff0c\u4ece\u6781\u9650\u7684\u89d2\u5ea6\u7406\u89e3\u65e0\u9650\u957f\u5355\u6446\u7684\u5468\u671f\u7b49\u76f8\u5173\u95ee\u9898\u00b7\u00b7\u00b7<\/p>\n","protected":false},"excerpt":{"rendered":"

JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c6\u671f\uff082025.4.29\uff09 \u4e8c\u4f53\u95ee\u9898\u4e0e\u7ea6\u5316\u8d28\u91cf JQX|Xiao \u4e00\u3001\u6c34\u5e73\u5f39\u7c27\u53cc\u7403\u7cfb\u7edf … \u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[9],"tags":[460],"class_list":["post-36727","post","type-post","status-publish","format-standard","hentry","category-jqx","tag-jqx"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/36727","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=36727"}],"version-history":[{"count":0,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/36727\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=36727"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=36727"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=36727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}