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1、论复摆振动的研究作者：白忠亮 学号：200702051006红河学院07物理系，蒙自 661100摘要：复摆对于某一间接测量量，要减小其随机误差的一个必要条件，就是要它具有较小的随机不确定度（通常以标准差表示）本实验中的三种解法，都具有典型性这里需要特别指出，使用最小二乘法处理适合，该方法适用的条件及误差分析。关键词：复摆 重力加速度 转动惯量 最小二乘法 引言：复摆实验是一个传统的实验，通常是研究周期与摆轴位置的关系，并测定重力加速度和转动惯量 原理 一个围绕定轴摆动的刚体就是复摆，当摆动的振幅甚小时，其振动周期T为 （1）式中I为复摆对回转轴O的转动惯量，为复摆的质量，为当地的重力加速度，
2、为摆的支点到摆的质心的距离（图（1） 又设复摆对通过质心G平行O轴的轴的转动惯量为，则 （2）而又可写成为，就是复摆对G轴的回转半径，由此可将式（l）改成为 （3） 实验内容1测量相应不同支点的周期abOGsh图（2）OGh图（1）支点位置，用从摆的一端a量度的距离s表示将支点由靠近a端开始，逐渐移向b端并测周期T，摆角小于5改变支点13次图（2）要求测得的周期T的相对误差小于0.5 2测定重心G的位置将复摆水平放在支架的刀刃上图（3），利用杠杆原理寻找G点的位置，要求的误差在1mm以内3求出各值对应的h值h均取正值），作Th图线图（4）4将式（3）改写成为 （4）TGhhab图（4）复摆支架
3、刀刃图（3） 令，则上式又成为 （5）从测量可得出n组（x，y）值，用最小二乘法求出拟合直线y=A+Bx的和，再由A、B求出g和k值，并计算g的不确定度最后求出实验数据用分析天平称量复摆的质量（分析天平的分度值）m=2200.0g用米尺测量,用秒表测量振动周期T米尺的分度值，秒表的分度值复摆的上端：，实验组i123456789104.0245.9048.1948.2548.0047.9448.0548.1048.1548.2048.0047.977.4842.4447.4347.4147.2247.4047.4747.3947.3547.3747.3047.2810.9838.9446.624
4、6.5346.7546.7046.7246.6846.6246.5846.6046.6514.4035.5245.9646.1946.2546.1946.2046.1846.1546.1046.0046.0417.8832.0445.7245.6945.6545.6945.6045.5845.5945.5345.5545.5021.3628.5645.6745.7145.6545.7245.7245.6845.7145.6545.7145.7024.8025.1245.5945.7545.7245.7045.7045.6545.6045.6745.6345.6528.3021.6246.384
5、6.3446.3446.3546.4246.4246.4046.3046.3446.3431.7118.2148.1648.0048.0648.0248.0548.0748.0848.1048.1348.1035.1414.7850.1950.3050.4450.3550.3850.2050.3050.2450.2050.2338.6211.3055.2555.2255.1655.1855.2255.2855.2555.2455.1855.1942.097.8363.9063.8463.9463.8563.8763.9063.8763.9263.9463.9045.524.4082.5082.
6、7282.6082.5582.5882.6682.6782.7082.5182.71复摆的下端：实验组i123456789104.0345.8348.1948.0648.1048.1548.1148.0648.1948.0848.1348.187.5042.3647.4747.4747.4547.4247.4047.3947.4247.4747.4047.4010.9238.9446.7546.7946.7046.7246.7346.7146.7546.7946.7746.7514.3835.4846.3246.1946.2046.2946.2546.3246.222746.2846.2717
7、.8432.0245.8845.9145.9545.8345.8645.8845.9045.9445.9145.8721.3028.5645.7545.7245.7845.7745.6845.8045.7245.7045.7545.7824.7625.1046.0345.9645.9045.9645.9545.9345.9845.9745.969628.2021.6646.7246.6646.6646.6546.7046.7246.7546.6746.6746.7231.7018.1648.1548.2248.2248.2548.1348.1548.1748.1448.2048.2435.14
8、14.7250.7850.7250.8050.7150.7250.7750.7550.7750.7450.7238.6011.2655.4755.5055.4455.4055.4555.5255.5055.4755.4655.4242.107.7663.9464.0664.0963.9064.0063.9064.0164.0564.0763.9545.534.3383.6583.8583.6083.6583.6883.7283.7783.7483.7083.68数据处理由以上数据作与数据表格如下：上端实验组i1234567891011121345.9042.4438.9435.5232.042
9、8.5625.1221.6218.2114.7811.307.834.401.6021.5791.5551.5381.5201.5231.5301.5451.6021.6761.8402.1302.754下端实验组i1234567891011121345.8342.3638.9435.4832.0228.5625.1021.6618.1614.7211.267.764.331.6041.5811.5581.5421.5301.5251.5321.5561.6061.6911.8492.1332.790根据求出各s值对应的h值作Th曲线（如下图）作出的Th曲线符合实验原理中Th曲线根据实验原理：
10、令y=h2，x=hT2。用最小二乘法处理拟合直线y=A+Bx的直线上端12345672106.811801.1541516.3241261.671026.562815.6736631.0144117.7979105.813194.1578984.0205774.0252266.2457558.80341上端8910111213467.4244331.6041218.4484127.6961.308919.3651.6074846.7342241.5166738.2572835.5239333.37187下端12345672100.3891794.371516.3241258.831025.28
11、815.6736630.01117.9122105.881494.5215584.3630774.9556266.4198558.9103下端8910111213469.1556329.7856216.6784126.787660.217618.748952.4418146.8389342.0915638.495735.3055933.70515对复摆的上端798.849（） 65.221（）9434.871（）5790779.151（）233709.152（）用最小二乘法求A和B的估计值和24.771（）-816.740（）相关系数的计算0.999860A和B的标准偏差的计算0.125（）8.821（）由，0.286m由，9.769（）0.180（）不确定度的计算0.125（）8.821（）不确定度的合成由，0.049（）由，0.030m由，0.038（）实验结果（重力加速度）（复摆对G轴的回转半径）（通过质心G平行o轴的轴的转动惯量）
