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1、复摆实验报告一、实验数据复摆质量m=396.71 g 复摆重心位置HG=0.00 cm 铜刀口质量m =6.30 g 表 1 数据记录、计算与列表h/cm 20T/s T/s h2/m2 T2|h|/(s2m) 28.16 25.0594 1.25297 0.07929856 0.442093364 27.16 24.8624 1.24312 0.07376656 0.419716336 26.12 24.6864 1.23432 0.06822544 0.397950179 25.16 24.5101 1.225505 0.06330256 0.377868606 24.12 24.3415
2、 1.217075 0.05817744 0.357282699 23.12 24.1924 1.20962 0.05345344 0.338287342 22.14 24.0407 1.202035 0.04901796 0.319898234 21.16 23.9264 1.19632 0.04477456 0.302838014 20.14 23.8218 1.19109 0.04056196 0.285725251 19.14 23.7382 1.18691 0.03663396 0.269635774 18.16 23.7012 1.18506 0.03297856 0.255033
3、084 17.14 23.6818 1.18409 0.02937796 0.240314649 16.16 23.72 1.186 0.02611456 0.227305914 15.18 23.7819 1.189095 0.02304324 0.214637142 14.16 23.9204 1.19602 0.02005056 0.20255368 13.16 24.1304 1.20652 0.01731856 0.191568871 12.16 24.4062 1.22031 0.01478656 0.18108143 11.14 24.7928 1.23964 0.0124099
4、6 0.171189197 10.14 25.319 1.26595 0.01028196 0.162506621 8.16 26.8804 1.34402 0.00665856 0.147401404 6.16 29.6492 1.48246 0.00379456 0.135377559 4.12 34.6873 1.734365 0.00169744 0.123930504 2.18 46.7125 2.335625 0.00047524 0.118922142 1.12 61.3588 3.06794 0.00012544 0.105417265 -28.28 25.0597 1.252
5、985 0.07997584 0.443987915 -27.28 24.8769 1.243845 0.07441984 0.422062625 -26.26 24.6732 1.23366 0.06895876 0.399655403 -25.28 24.4948 1.22474 0.06390784 0.379196983 -24.28 24.3283 1.216415 0.05895184 0.359262772 -23.28 24.1769 1.208845 0.05419584 0.340192091 -22.29 24.0344 1.20172 0.04968441 0.3218
6、96791 -21.28 23.9301 1.196505 0.04528384 0.304649633 -20.28 23.8118 1.19059 0.04112784 0.287469922 -19.29 23.749 1.18745 0.03721041 0.271996234 -18.28 23.71 1.1855 0.03341584 0.256908994 -17.29 23.6919 1.184595 0.02989441 0.242624573 -16.28 23.7116 1.18558 0.02650384 0.22883167 -15.29 23.7244 1.1862
7、2 0.02337841 0.215148325 -14.29 23.9142 1.19571 0.02042041 0.204307332 -13.28 24.1227 1.206135 0.01763584 0.193192346 -12.28 24.4301 1.221505 0.01507984 0.183226744 -11.29 24.7789 1.238945 0.01274641 0.173299774 -10.28 25.301 1.26505 0.01056784 0.164516134 -9.29 25.9778 1.29889 0.00863041 0.15673300
8、5 -7.29 27.3267 1.366335 0.00531441 0.13609492 -5.29 31.8271 1.591355 0.00279841 0.133964528 -3.29 39.3259 1.966295 0.00108241 0.127201797 -1.28 61.9938 3.09969 0.00016384 0.1229834 法一：直线拟合分别对左半部分和右半部分的T2h-h2关系作图，剔除无效数据，做线性拟合。左半部分如图1 所示：斜率 k1=4.1123 s2/m ，截距 b1=0.1182 s2m ，相关系数R12=0.999 计算得：2121/600
9、.94) 1 (gsmk右半部分如图2 所示：斜率 k2=4.037s2/m ，截距 b2=0.1215s2m，相关系数R22=0.9998 计算得：2222/779.94)2(gsmk对以上两次测量求得的g 做加权平均，权重比正比于12)-1 R（，得：2 2 22 112 112 2 1/749. 9)1()1 ()2()1()1()1(gsmRRgRgRy = 4.112x + 0.118 R2 = 0.99900.050.10.150.20.250.30.350.40.450.500.010.020.030.040.050.060.070.080.09T2h/(s2m)h2/m2图1
10、左半T2h-h2直线图y = 4.037x + 0.121 R2 = 0.99900.050.10.150.20.250.30.350.40.450.500.010.020.030.040.050.060.070.080.09T2h/(s2m)h2/m2图2 右半T2h-h2直线图复摆对重心的转动惯量：32110994. 24b) 1(GI3 2210078.34b)2(GI32 22 12 12 2 G10064.3)1()1 ()2()1() 1()1(IRRIRIRGG310779.2mG GIR法二：近似共轭点法T-h 关系如图3 所示，在图中选择三组近似共轭点，选点具体信息如表2 所
11、示：表 2 共轭点选取hL/cm TL/s hR/cm TR/s g2/m s-223.28 1.208845 13.16 1.20652 9.864 17.29 1.184595 17.14 1.18409 9.690 11.29 1.238945 26.12 1.23432 9.658 00.511.522.533.5-40-30-20-10010203040T/sh2/cm图3 T-h关系图h1/cm 所以，2 2/737.93658.9690.9864.9gsm法三：共轭点法从图 4 上读出 T=1.22000 s除的两对共轭点的横坐标（见表3）表 3 T=1.22000处两对共轭点位置cm73.36221LLL2 223/742.94gsmTL1.161.181.21.221.241.261.281.3-30-20-100102030坐标轴标题图4 T-h关系局部图hL1/cm hR1/cm L1/cm hL2/cm hR2/cm L2/cm 24.58 12.17 36.75 12.29 24.42 36.71
