{"id":49412,"date":"2026-10-22T10:39:46","date_gmt":"2026-10-22T02:39:46","guid":{"rendered":"https:\/\/www.qiusir.com\/?p=49412"},"modified":"2026-10-22T10:40:26","modified_gmt":"2026-10-22T02:40:26","slug":"%e7%89%a9%e7%90%86%e4%b8%ad%e7%9a%84%e8%b0%83%e5%92%8c%e5%b9%b3%e5%9d%87","status":"publish","type":"post","link":"https:\/\/www.qiusir.com\/?p=49412","title":{"rendered":"\u7269\u7406\u4e2d\u7684\u8c03\u548c\u5e73\u5747"},"content":{"rendered":"

JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c37\u671f\uff082026.10.15\uff09
\n\"\"\u7269\u7406\u4e2d\u7684\u8c03\u548c\u5e73\u5747<\/strong>
\n\"\"
\n\/\u5f15\u9898\uff1a\u53cc\u5c42\u4ecb\u8d28\u89c6\u6df1\u95ee\u9898<\/p>\n

\u5f53\u6211\u4eec\u4fef\u89c6\u6c34\u9762\u7684\u65f6\u5019\uff0c\u5165\u5c04\u89d2\u4e0e\u6298\u5c04\u89d2\u90fd\u5f88\u5c0f\uff0c\u8fd9\u65f6\u6298\u5c04\u5b9a\u5f8b\u53ef\u505a\u5c0f\u89d2\u8fd1\u4f3c $\\sin\\theta \\approx \\tan\\theta$\u3002\u5f53\u4ece\u6298\u5c04\u7387\u4e3a $n_0$ \u7684\u73af\u5883\u4e2d\u4fef\u89c6\u539a\u5ea6\u5206\u522b\u4e3a $h_1, h_2$\u3001\u6298\u5c04\u7387\u5206\u522b\u4e3a $n_1, n_2$ \u7684\u53cc\u5c42\u4ecb\u8d28\u65f6\uff0c\u6839\u636e\u6298\u5c04\u5b9a\u5f8b\u548c\u51e0\u4f55\u89c4\u5f8b\uff0c\u5229\u7528\u5149\u7ebf\u5728\u4e24\u4e2a\u4ecb\u8d28\u4e2d\u6c34\u5e73\u504f\u79fb\u91cf\u7684\u603b\u548c\u7b49\u4e8e\u6210\u50cf\u5149\u7ebf\u7684\u6c34\u5e73\u6295\u5f71\uff0c\u5728\u4e24\u4e2a\u4ecb\u8d28\u4e2d\u603b\u89c6\u6df1\u6ee1\u8db3 $\\frac{h_0}{n_0} = \\frac{h_1}{n_1} + \\frac{h_2}{n_2}$\u3002\u82e5\u4eba\u5728\u7a7a\u6c14\u4e2d\u89c2\u5bdf\uff08$n_0 = 1$\uff09\uff0c\u5219\u7b49\u6548\u89c6\u6df1\u76f4\u63a5\u4e3a $h_0 = \\frac{h_1}{n_1} + \\frac{h_2}{n_2}$\uff0c\u8fd9\u5176\u4e2d\u7684\u5f62\u5f0f\u5728\u6570\u5b66\u4e0a\u79f0\u4e3a\u8c03\u548c\u5e73\u5747\u6570\uff0c\u800c\u8fd9\u79cd\u5f62\u5f0f\u5728\u7269\u7406\u4e2d\u8fd8\u6709\u8bb8\u591a\u4f8b\u5b50\uff08\u6bd4\u5982\u53d8\u538b\u5668\uff0c\u539f\u7ebf\u5708$n_0$\uff0c\u526f\u7ebf\u5708$n_1$\uff0c$n_2$\uff0c\u5bf9\u5e94\u7535\u963b$R_1$,$R_2$\uff0c\u5bf9\u539f\u7ebf\u5708\u6765\u8bf4\u7b49\u6548\u7535\u963b$\\frac{n_0^2}{R_0}=\\frac{n_1^2}{R_1}+\\frac{n_2^2}{R_2}$\uff09\uff0c\u4e0b\u9762\u5c31\u76f8\u5173\u9000\u5316\u5f0f\u6837\u4e00\u4e00\u4e3e\u4f8b\u3002<\/p>\n

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\n1. \u7535\u963b\u5e76\u8054<\/p>\n

\u5728\u7535\u963b\u5e76\u8054\u7535\u8def\u4e2d\uff0c\u5404\u652f\u8def\u7535\u52bf\u5dee\u4e25\u683c\u76f8\u7b49\uff0c\u5e72\u8def\u603b\u7535\u6d41\u7b49\u4e8e\u5404\u652f\u8def\u7535\u6d41\u4e4b\u548c $I = I_1 + I_2$\u3002\u7531\u6b27\u59c6\u5b9a\u5f8b $I = \\frac{U}{R}$ \u7ea6\u53bb\u516c\u7535\u538b $U$\uff0c\u5373\u5f97\u7b49\u6548\u603b\u7535\u963b\u7684\u8c03\u548c\u5e73\u5747\u5f62\u5f0f $\\frac{1}{R} = \\frac{1}{r_1} + \\frac{1}{r_2}$\uff0c\u5316\u7b80\u4e3a $R = \\frac{r_1 r_2}{r_1 + r_2}$\u3002<\/p>\n

2. \u7535\u963b\u4e32\u8054
\n\u5728\u7535\u963b\u4e32\u8054\u7535\u8def\u4e2d\u5404\u5904\u7535\u6d41\u6052\u5b9a\uff0c\u603b\u7aef\u7535\u538b\u7b49\u4e8e\u5404\u5206\u6bb5\u7535\u538b\u4e4b\u548c $U = U_1 + U_2$\u3002\u82e5\u4ee5\u8868\u5f81\u5bfc\u7535\u80fd\u529b\u7684\u7535\u5bfc $G = \\frac{1}{R}$\uff08\u6ee1\u8db3 $U = \\frac{I}{G}$\uff09\u63cf\u8ff0\uff0c\u7ea6\u53bb\u7535\u6d41 $I$ \u540e\uff0c\u7b49\u6548\u7535\u5bfc\u5448\u73b0\u8c03\u548c\u5e73\u5747\u5f62\u5f0f $\\frac{1}{G} = \\frac{1}{g_1} + \\frac{1}{g_2}$\uff0c\u5316\u7b80\u4e3a $G = \\frac{g_1 g_2}{g_1 + g_2}$\u3002
\n\"\"
\n3. \u7535\u5bb9\u4e32\u8054<\/p>\n

\u7535\u5bb9\u4e32\u8054\u65f6\u56e0\u9759\u7535\u611f\u5e94\u4f7f\u5404\u6781\u677f\u7535\u8377\u91cf\u5904\u5904\u76f8\u7b49\uff0c\u4e24\u7aef\u603b\u7535\u538b\u7b49\u4e8e\u5404\u7535\u5bb9\u5206\u538b\u4e4b\u548c $U = U_1 + U_2$\u3002\u7531\u7535\u5bb9\u5b9a\u4e49\u5f0f $U = \\frac{Q}{C}$ \u7ea6\u53bb\u7535\u8377\u91cf $Q$\uff0c\u5f97\u5230\u7b49\u6548\u7535\u5bb9\u7684\u8c03\u548c\u5e73\u5747\u5f62\u5f0f $\\frac{1}{C} = \\frac{1}{C_1} + \\frac{1}{C_2}$\uff0c\u5316\u7b80\u4e3a $C = \\frac{C_1 C_2}{C_1 + C_2}$\u3002<\/p>\n

4. \u5f39\u7c27\u4e32\u8054<\/p>\n

\u8f7b\u8d28\u5f39\u7c27\u9996\u5c3e\u4e32\u63a5\u65f6\u5185\u90e8\u5404\u5904\u5f20\u529b\u5904\u5904\u76f8\u7b49\uff0c\u5916\u529b\u62c9\u52a8\u4e0b\u7684\u603b\u4f38\u957f\u91cf\u7b49\u4e8e\u5404\u6bb5\u5f62\u53d8\u91cf\u4e4b\u548c $x = x_1 + x_2$\u3002\u7531\u80e1\u514b\u5b9a\u5f8b $x = \\frac{F}{k}$ \u7ea6\u53bb\u62c9\u529b $F$\uff0c\u5f97\u5230\u7b49\u6548\u52b2\u5ea6\u7cfb\u6570\u7684\u8c03\u548c\u5e73\u5747\u5f62\u5f0f $\\frac{1}{k} = \\frac{1}{k_1} + \\frac{1}{k_2}$\uff0c\u5316\u7b80\u4e3a $k = \\frac{k_1 k_2}{k_1 + k_2}$\u3002<\/p>\n

5. \u7535\u611f\u5e76\u8054<\/p>\n

\u81ea\u611f\u7ebf\u5708\u5e76\u8054\u65f6\u5404\u652f\u8def\u4e24\u7aef\u77ac\u65f6\u611f\u5e94\u7535\u52a8\u52bf\u76f8\u540c\uff0c\u5e72\u8def\u603b\u7535\u6d41\u53d8\u5316\u7387\u7b49\u4e8e\u5404\u652f\u8def\u4e4b\u548c $\\frac{\\mathrm{d}I}{\\mathrm{d}t} = \\frac{\\mathrm{d}I_1}{\\mathrm{d}t} + \\frac{\\mathrm{d}I_2}{\\mathrm{d}t}$\u3002\u7531\u7535\u78c1\u611f\u5e94\u89c4\u5f8b $U = L \\frac{\\mathrm{d}I}{\\mathrm{d}t}$ \u7ea6\u53bb\u7535\u52a8\u52bf $U$\uff0c\u5f97\u5230\u7b49\u6548\u81ea\u611f\u7684\u8c03\u548c\u5e73\u5747\u5f62\u5f0f $\\frac{1}{L} = \\frac{1}{L_1} + \\frac{1}{L_2}$\uff0c\u5316\u7b80\u4e3a $L = \\frac{L_1 L_2}{L_1 + L_2}$\u3002<\/p>\n

6. \u7b49\u8def\u7a0b\u5f80\u8fd4\u5e73\u5747\u901f\u5ea6<\/p>\n

\u8d28\u70b9\u5728\u5355\u7a0b\u8def\u7a0b\u4e3a $S$ \u7684\u4e24\u5730\u95f4\u5f80\u8fd4\uff0c\u53bb\u7a0b\u901f\u5ea6\u4e3a $v_1$\uff0c\u8fd4\u7a0b\u901f\u5ea6\u4e3a $v_2$\u3002\u5168\u8fc7\u7a0b\u5e73\u5747\u901f\u7387\u4e3a\u603b\u8def\u7a0b\u4e0e\u603b\u65f6\u95f4\u4e4b\u6bd4 $\\bar{v} = \\frac{2S}{t_1 + t_2}$\uff0c\u5c06\u5206\u6bb5\u65f6\u95f4 $t_1 = \\frac{S}{v_1}, t_2 = \\frac{S}{v_2}$ \u4ee3\u5165\u5e76\u7ea6\u53bb\u8def\u7a0b $S$\uff0c\u5373\u5f97\u5f80\u8fd4\u5e73\u5747\u901f\u5ea6\u6ee1\u8db3\u8c03\u548c\u5e73\u5747\u516c\u5f0f $\\frac{2}{\\bar{v}} = \\frac{1}{v_1} + \\frac{1}{v_2}$\uff0c\u5316\u7b80\u4e3a $\\bar{v} = \\frac{2 v_1 v_2}{v_1 + v_2}$\u3002<\/p>\n

7. \u7b49\u8d28\u91cf\u7269\u4f53\u5e73\u5747\u5bc6\u5ea6<\/p>\n

\u5c06\u5bc6\u5ea6\u5206\u522b\u4e3a $\\rho_1, \\rho_2$ \u7684\u4e24\u79cd\u7269\u6599\u6309\u76f8\u540c\u8d28\u91cf $m$ \u5747\u5300\u6df7\u5408\uff08\u4e0d\u8003\u8651\u4f53\u79ef\u6536\u7f29\uff09\u3002\u6df7\u5408\u7269\u603b\u4f53\u79ef\u4e3a\u5404\u7ec4\u5206\u4f53\u79ef\u4e4b\u548c $V = V_1 + V_2 = \\frac{m}{\\rho_1} + \\frac{m}{\\rho_2}$\uff0c\u7531\u5e73\u5747\u5bc6\u5ea6\u5b9a\u4e49 $\\bar{\\rho} = \\frac{2m}{V_1 + V_2}$ \u7ea6\u53bb\u8d28\u91cf $m$\uff0c\u5373\u5f97\u7b49\u8d28\u91cf\u6df7\u5408\u65f6\u7684\u5e73\u5747\u5bc6\u5ea6\u5448\u73b0\u8c03\u548c\u5e73\u5747\u503c $\\bar{\\rho} = \\frac{2\\rho_1 \\rho_2}{\\rho_1 + \\rho_2}$\u3002
\n\"\"
\n8. \u53cc\u661f\u9006\u5411\u516c\u8f6c\u5171\u7ebf\u65f6\u95f4\u95f4\u9694<\/p>\n

\u4e24\u661f\u4f53\u7ed5\u4e2d\u5fc3\u5929\u4f53\u5728\u4e0d\u540c\u8f68\u9053\u4e0a\u53cd\u5411\u516c\u8f6c\uff0c\u516c\u8f6c\u5468\u671f\u5206\u522b\u4e3a $T_1, T_2$\u3002\u9006\u5411\u76f8\u5411\u8fd0\u52a8\u7684\u76f8\u5bf9\u89d2\u901f\u5ea6\u4e3a\u5404\u81ea\u6807\u91cf\u4e4b\u548c $\\omega_{\\text{\u76f8\u5bf9}} = \\omega_1 + \\omega_2$\uff0c\u76f8\u9047\u65f6\u8f6c\u8fc7\u7684\u76f8\u5bf9\u89d2\u4f4d\u79fb\u4e3a $2\\pi$\u3002\u7531 $(\\omega_1 + \\omega_2)t = 2\\pi$ \u4ee3\u5165 $\\omega = \\frac{2\\pi}{T}$ \u5e76\u7ea6\u53bb $2\\pi$\uff0c\u5373\u5f97\u76f8\u9047\u65f6\u95f4\u95f4\u9694\u6ee1\u8db3\u8c03\u548c\u5e73\u5747\u5f62\u5f0f $\\frac{1}{t} = \\frac{1}{T_1} + \\frac{1}{T_2}$\uff0c\u5316\u7b80\u4e3a $t = \\frac{T_1 T_2}{T_1 + T_2}$\u3002
\n\"\"
\n9. \u67ef\u5c3c\u5e0c\u5b9a\u7406\u4e0e\u7ea6\u5316\u8d28\u91cf<\/p>\n

\u6839\u636e\u67ef\u5c3c\u5e0c\u5b9a\u7406\uff0c\u53cc\u8d28\u70b9\u7cfb\u7edf\u7684\u603b\u52a8\u80fd\u53ef\u5206\u89e3\u4e3a\u968f\u8d28\u5fc3\u5e73\u52a8\u52a8\u80fd\u4e0e\u76f8\u5bf9\u8d28\u5fc3\u52a8\u80fd\u4e4b\u548c $E_k = \\frac{1}{2}(m_1 + m_2)v_c^2 + E_{k,\\text{\u76f8\u5bf9}}$\u3002\u5c06\u76f8\u5bf9\u8d28\u5fc3\u7684\u901f\u5ea6\u7528\u4e24\u7269\u4f53\u76f8\u5bf9\u901f\u5ea6 $v_r = v_1 – v_2$ \u5c55\u5f00\u540e\uff0c\u76f8\u5bf9\u52a8\u80fd\u6574\u7406\u4e3a\u5355\u4f53\u5f62\u5f0f $E_{k,\\text{\u76f8\u5bf9}} = \\frac{1}{2}\\mu v_r^2$\uff0c\u5176\u4e2d\u7ea6\u5316\u8d28\u91cf\u6ee1\u8db3\u8c03\u548c\u6c42\u548c $\\frac{1}{\\mu} = \\frac{1}{m_1} + \\frac{1}{m_2}$\uff0c\u5316\u7b80\u4e3a $\\mu = \\frac{m_1 m_2}{m_1 + m_2}$\u3002
\n\"\"
\n10. \u6c34\u5e73\u684c\u9762\u6ed1\u5757\u8fde\u63a5\u4f53\u7cfb\u7edf<\/p>\n

\u8d28\u91cf\u4e3a $M$ \u7684\u6ed1\u5757\u5728\u5149\u6ed1\u6c34\u5e73\u684c\u9762\u4e0a\u7ecf\u684c\u89d2\u5b9a\u6ed1\u8f6e\u8fde\u63a5\u7ad6\u76f4\u60ac\u6302\u7684\u8d28\u91cf\u4e3a $m$ \u7684\u5c0f\u7269\u5757\u3002\u8054\u7acb\u6c34\u5e73\u65b9\u5411\u725b\u987f\u65b9\u7a0b $T = Ma$ \u4e0e\u60ac\u6302\u65b9\u5411\u65b9\u7a0b $mg – T = ma$ \u6d88\u53bb\u52a0\u901f\u5ea6\uff0c\u89e3\u5f97\u8f7b\u7ef3\u5f20\u529b\u4e3a $T = \\frac{Mm}{M+m}g = \\mu g$\uff0c\u5f20\u529b\u5927\u5c0f\u4e25\u683c\u7b49\u4e8e\u7ea6\u5316\u8d28\u91cf\u4e58\u4ee5\u91cd\u529b\u52a0\u901f\u5ea6\u3002<\/p>\n

11. \u963f\u7279\u4f0d\u5fb7\u673a<\/p>\n

\u8f7b\u8d28\u5b9a\u6ed1\u8f6e\u4e24\u7aef\u5206\u522b\u7ad6\u76f4\u60ac\u6302\u8d28\u91cf\u4e3a $M$ \u4e0e $m$ \u7684\u4e24\u91cd\u7269\u3002\u8054\u7acb\u8fd0\u52a8\u65b9\u7a0b $Mg – T = Ma$ \u4e0e $T – mg = ma$ \u6d88\u53bb\u52a0\u901f\u5ea6\uff0c\u89e3\u5f97\u8f7b\u7ef3\u5f20\u529b\u52a0\u500d\u4e3a $T = \\frac{2Mm}{M+m}g = 2\\mu g$\uff0c\u8be5\u5f20\u529b\u7cbe\u786e\u7b49\u4e8e\u4e24\u7269\u4f53\u9759\u6b62\u91cd\u529b $G_1 = Mg, G_2 = mg$ \u7684\u6807\u51c6\u8c03\u548c\u5e73\u5747\u6570 $\\frac{1}{T} = \\frac{1}{2}(\\frac{1}{G_1} + \\frac{1}{G_2})$\u3002
\n\"\"
\n12. \u6c34\u5e73\u53cc\u7269\u5757\u5f39\u7c27\u632f\u5b50\u7cfb\u7edf<\/p>\n

\u5149\u6ed1\u6c34\u5e73\u9762\u4e0a\u8d28\u91cf\u4e3a $m_1, m_2$ \u7684\u4e24\u7269\u5757\u7531\u52b2\u5ea6\u7cfb\u6570\u4e3a $k$ \u7684\u8f7b\u5f39\u7c27\u8fde\u63a5\uff0c\u8d28\u5fc3\u4fdd\u6301\u9759\u6b62\u3002\u7531\u4e24\u7269\u5757\u53d7\u529b\u65b9\u7a0b\u5f97\u76f8\u5bf9\u4f4d\u79fb\u5fae\u5206\u65b9\u7a0b $\\ddot{x} = -k(\\frac{1}{m_1} + \\frac{1}{m_2})x = -\\frac{k}{\\mu}x$\uff0c\u53cc\u4f53\u76f8\u5bf9\u632f\u52a8\u7b49\u6548\u4e3a\u5355\u7aef\u56fa\u5b9a\u4e8e\u8d28\u5fc3\u7684\u7ea6\u5316\u8d28\u91cf\u5355\u632f\u5b50\uff0c\u5176\u632f\u52a8\u5468\u671f\u4e3a $T = 2\\pi\\sqrt{\\frac{\\mu}{k}} = 2\\pi\\sqrt{\\frac{m_1 m_2}{(m_1 + m_2)k}}$\u3002<\/p>\n

13. \u53cc\u5f39\u7c27\u53cc\u7269\u5757\u632f\u52a8\u7cfb\u7edf<\/p>\n

\u4e24\u5f39\u7c27\u7531\u8de8\u8fc7\u4e24\u5b9a\u6ed1\u8f6e\u7684\u8f7b\u7ef3\u76f8\u8fde\uff0c\u4e0b\u7aef\u5206\u522b\u60ac\u6302\u8d28\u91cf $m_1, m_2$\u3002\u8f7b\u7ef3\u5f20\u529b\u5904\u5904\u76f8\u7b49\u4f7f\u4e24\u5f39\u7c27\u603b\u4f38\u957f\u7b49\u4e8e\u5404\u81ea\u4f38\u957f\u4e4b\u548c\uff0c\u7b49\u6548\u521a\u5ea6\u4e3a\u4e32\u8054\u5f62\u5f0f $k_{\\text{\u7b49\u6548}} = \\frac{k_1 k_2}{k_1 + k_2}$\uff1b\u4e24\u7aef\u8d28\u91cf\u76f8\u5bf9\u8fd0\u52a8\u60ef\u6027\u7531\u7ea6\u5316\u8d28\u91cf $\\mu = \\frac{m_1 m_2}{m_1 + m_2}$ \u51b3\u5b9a\uff0c\u7cfb\u7edf\u632f\u52a8\u56fa\u6709\u9891\u7387\u76f4\u63a5\u7531\u521a\u5ea6\u4e0e\u7ea6\u5316\u8d28\u91cf\u5171\u540c\u7ed9\u51fa $\\omega = \\sqrt{\\frac{k_{\\text{\u7b49\u6548}}}{\\mu}} = \\sqrt{\\frac{k_1 k_2(m_1 + m_2)}{(k_1 + k_2)m_1 m_2}}$\u3002
\n\"\"
\n14. \u5149\u5b66\u900f\u955c\u6210\u50cf<\/p>\n

\u51f8\u900f\u955c\u6210\u50cf\u7684\u9ad8\u65af\u7269\u50cf\u516c\u5f0f $\\frac{1}{u} + \\frac{1}{v} = \\frac{1}{f}$ \u53ef\u53d8\u5f62\u4e3a $2f = \\frac{2uv}{u+v}$\uff0c\u8868\u660e\u4e8c\u500d\u7126\u8ddd\u7b49\u4e8e\u7269\u8ddd\u4e0e\u50cf\u8ddd\u7684\u8c03\u548c\u5e73\u5747\u6570\uff0c\u7ed3\u5408\u5747\u503c\u4e0d\u7b49\u5f0f\u53ef\u76f4\u63a5\u5bfc\u51fa\u7269\u4e0e\u5b9e\u50cf\u95f4\u6700\u5c0f\u8ddd\u79bb\u5b9a\u7406 $u+v \\ge 4f$\uff1b\u800c\u4e24\u8584\u900f\u955c\u5bc6\u63a5\u8d34\u5408\u65f6\uff0c\u504f\u6298\u5149\u7ebf\u7684\u5149\u7126\u5ea6\u76f4\u63a5\u76f8\u52a0 $\\Phi = \\Phi_1 + \\Phi_2$\uff0c\u5176\u7b49\u6548\u590d\u5408\u7126\u8ddd\u540c\u6837\u6ee1\u8db3\u8c03\u548c\u5e73\u5747\u5173\u7cfb $\\frac{1}{f} = \\frac{1}{f_1} + \\frac{1}{f_2}$\uff0c\u5316\u7b80\u4e3a $f = \\frac{f_1 f_2}{f_1 + f_2}$\u3002
\n\"\"
\n15. \u5b8f\u89c2\u8d85\u957f\u5355\u6446\u7cfb\u7edf<\/p>\n

\u5f53\u5355\u6446\u6446\u957f $L$ \u8fbe\u5230\u5730\u7403\u534a\u5f84 $R$ \u7684\u5b8f\u89c2\u91cf\u7ea7\u65f6\uff0c\u6446\u7ebf\u504f\u89d2 $\\alpha \\approx \\frac{x}{L}$ \u4e0e\u6307\u5411\u5730\u5fc3\u7684\u5f15\u529b\u504f\u89d2 $\\beta \\approx \\frac{x}{R}$ \u5171\u540c\u63d0\u4f9b\u6307\u5411\u4e2d\u8f74\u7684\u6062\u590d\u529b\uff0c\u7b49\u6548\u56de\u590d\u529b\u5e38\u6570\u4e3a $k_{\\text{\u7b49\u6548}} = mg(\\frac{1}{L} + \\frac{1}{R})$\u3002\u7cfb\u7edf\u7684\u7b49\u6548\u6446\u957f\u6ee1\u8db3\u8c03\u548c\u6c42\u548c $\\frac{1}{L_{\\text{\u7b49\u6548}}} = \\frac{1}{L} + \\frac{1}{R}$\uff0c\u632f\u52a8\u5468\u671f\u4e3a $T = 2\\pi\\sqrt{\\frac{1}{g(\\frac{1}{L} + \\frac{1}{R})}} = 2\\pi\\sqrt{\\frac{LR}{(L+R)g}}$\uff0c\u5728 $L \\to \\infty$ \u65f6\u6781\u9650\u5468\u671f\u4e3a\u8212\u62c9\u5468\u671f $T = 2\\pi\\sqrt{\\frac{R}{g}} \\approx 84.4\\text{ min}$\u3002
\n\"\"
\n16. \u5929\u4f53\u53cc\u661f\u7cfb\u7edf\u4e0e<\/p>\n

\u8d28\u91cf\u4e3a $m_1, m_2$ \u7684\u4e24\u661f\u76f8\u8ddd $L$ \u7ed5\u516c\u5171\u8d28\u5fc3\u516c\u8f6c\uff0c\u8f68\u9053\u534a\u5f84\u53cd\u6bd4\u4e8e\u8d28\u91cf\u3002\u5c06\u534a\u5f84 $r_1 = \\frac{m_2}{m_1 + m_2}L$ \u4ee3\u5165\u5411\u5fc3\u529b\u65b9\u7a0b $G\\frac{m_1 m_2}{L^2} = m_1 \\omega^2 r_1$\uff0c\u5411\u5fc3\u529b\u9879\u5316\u7b80\u4e3a $F = \\mu \\omega^2 L$\uff0c\u5176\u4e2d\u7ea6\u5316\u8d28\u91cf\u6ee1\u8db3 $\\frac{1}{\\mu} = \\frac{1}{m_1} + \\frac{1}{m_2}$\uff1b\u8be5\u53cc\u661f\u7cfb\u7edf\u5b8c\u5168\u7b49\u6548\u4e3a\u4e2d\u5fc3\u56fa\u5b9a\u603b\u8d28\u91cf $M = m_1 + m_2$\uff0c\u7531\u865a\u62df\u5355\u4f53 $\\mu$ \u5728\u534a\u5f84\u4e3a $L$ \u7684\u8f68\u9053\u4e0a\u8fd0\u884c\u7684\u5f00\u666e\u52d2\u5355\u4f53\u6a21\u578b\u3002<\/p>\n

\"\"
JQX|Xiao<\/center>
\n\u4e0b\u671f\u9884\u544a\uff1a
\n36\u671f\u91d1\u5e08\u5e26\u9886\u6211\u4eec\u9886\u7565\u4e86\u62c9\u683c\u6717\u65e5\u70b9\u7684\u4ee3\u6570\u4e4b\u7f8e\uff0c\u4e0b\u671f\u6211\u4eec\u7ee7\u7eed\u4ece\u51e0\u4f55\u89d2\u5ea6\u62c6\u89e3L4\uff0cL5\u70b9\u7b49\u8fb9\u4e09\u89d2\u5f62\u7684\u6210\u56e0\uff0c\u540c\u65f6\u5728\u65cb\u8f6c\u53c2\u8003\u7cfb\u5f15\u5165\u6709\u6548\u52bf\u80fd\u66f2\u9762\uff0c\u7ed3\u5408\u79d1\u91cc\u5965\u5229\u529b\u5206\u6790\u7a33\u5b9a\u6027\u95ee\u9898\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

JQX\/\u8fdb\u53d6\u82af \u5e2d\u660e\u7eb3\u7b2c37\u671f\uff082026.10.15\uff09 \u7269\u7406\u4e2d\u7684\u8c03\u548c\u5e73\u5747 \/\u5f15\u9898\uff1a\u53cc\u5c42\u4ecb\u8d28\u89c6\u6df1\u95ee\u9898 \u5f53\u6211\u4eec\u4fef\u89c6 … \u9605\u8bfb\u66f4\u591a<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"image","meta":{"ngg_post_thumbnail":0,"footnotes":""},"categories":[9],"tags":[460,247],"class_list":["post-49412","post","type-post","status-publish","format-image","hentry","category-jqx","tag-jqx","tag-physics","post_format-post-format-image"],"_links":{"self":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/49412","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=49412"}],"version-history":[{"count":19,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/49412\/revisions"}],"predecessor-version":[{"id":49464,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=\/wp\/v2\/posts\/49412\/revisions\/49464"}],"wp:attachment":[{"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=49412"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=49412"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.qiusir.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=49412"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}