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清华大学
阻尼振动与受迫振动实验物理实验简要报告 班级XX学号 结稿日期：
阻尼振动与受迫振动实验报告（简要报告）
一、阻尼振动实验数据记录及处理
1、测量最小阻尼(阻尼0)时的阻尼比?和固有角频率?0
?n??50?I?int???int???25
?2??2?序号 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ?（?）129 128 127 127 125 125 124 123 122 121 121 120 119 118 117 yi?ln?i 4.859812404 4.852030264 4.844187086 4.844187086 4.828313737 4.828313737 4.820281566 4.812184355 4.804021045 4.795790546 4.795790546 4.787491743 4.779123493 4.770684624 4.762173935 序号 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 ?（?）110 109 108 108 107 106 106 104 103 103 102 102 101 100 100 yi?ln?i 4.700480366 4.691347882 4.682131227 4.682131227 4.672828834 4.663439094 4.663439094 4.644390899 4.634728988 4.634728988 4.624972813 4.624972813 4.615120517 4.605170186 4.605170186 Di?yi?25?yi -0.159332039 -0.160682382 -0.162055859 -0.162055859 -0.155484903 -0.164874643 -0.156842471 -0.167793456 -0.169292057 -0.161061557 -0.170817732 -0.162518929 -0.164002976 -0.165514438 -0.157003749 ..
16 17 18 19 20 21 22 23 24 25 118 117 116 115 114 114 113 112 112 110 4.770684624 4.762173935 4.753590191 4.744932128 4.736198448 4.736198448 4.727387819 4.718498871 4.718498871 4.700480366 41 42 43 44 45 46 47 48 49 50 99 98 98 97 96 96 95 94 94 93 4.59511985 4.584967479 4.584967479 4.574710979 4.564348191 4.564348191 4.553876892 4.543294782 4.543294782 4.532599493 -0.175564774 -0.177206456 -0.168622712 -0.17022115 -0.171850257 -0.171850257 -0.173510927 -0.175204089 -0.175204089 -0.167880873 -4.166448636 -0.166657945 ?D ii?1ID 于是得到： 11I1Ib?D?2?(yi?I?yi)?2?(ln?i?I?ln?i)IIi?1Ii?1??b?1I1-4.166448636?3?(ln??ln?)???6.666317818?10?i?25i252i?125225
?(D?D)i2/(I?1)?125?(D?D)i2/(25?1)?2.565475395?10?4
由b??2????2?1??0.5得到：
b2(?6.666317818?10?3)2?3????1.060976836?10 222?324π?b4?π?(?6.666317818?10)..
d?4?22???(?b)??b223/2db(4??b)?4?23/22?32?4??(?6.666317818?10)????4.083074011?10?5?2.565475395?10?4
从而可得??（1.061?0.041）?10-3。 序号 1 14.926 2 14.935 3 14.944 4 14.951 5 14.958 Ti?10Td/s 由上表，可得均值Td?1.49428s。
?Td?1.49428?10-5+0.001=1.0149428?10-3s
?0?2?Td1??2??2???2??1.49428?1??1.06?10-3??
???4.204826965s?1??0??Td????????????2?0??Td??1??222??3?1.0149428?10-3??1.060976836?10-3???0.04?10? ???2?3?1.49428???1?1.060976836?10?????6.792186217?10-4角频率的不确定度为：??0??02??0?0?2.855996775?10-3?0.0029s?1
?1由此，角频率为：?0??4.2048?0.0029?s
2、测量其他2种阻尼的相关振动参数。 （1）阻尼1
?n??10?I?int???int???5
?2??2?..
序号 1 2 3 4 5 ?（?） 105 96 88 80 73 yi?ln?i序号 6 7 8 9 10 ?（?） 67 61 56 50 46 yi?ln?i Di?yi?5?yi -0.449267731 -0.453474327 -0.451985123 -0.470003630 -0.461818045 -2.286548856 4.653960350 4.564348191 4.477336814 4.382026635 4.290459441 4.204692619 4.110873864 4.025351691 3.912024005 3.828641396 ?Di?1Ii D 11I1Ib?D?2?(yi?I?yi)?2?(ln?i?I?ln?i)IIi?1Ii?1??b?1I-0.457309771 1-2.286548856?(ln??ln?)???0.09146195424?i?5i52i?152155
?(Di?D)2/(I?1)??(D?D)i2/(5?1)?0.001700575?0.0017
由b??2????2?1??0.5得到：
b2(?0.09146195424)2????0.0145550801322224π?b4?π?(?0.09146195424)
4?24?2?d???????b???b??0.0017005753232222?db? ?4?2???0.09146195424???4??b????2.705689144?10?4可得阻尼比：??（1.456?0.027）?10-2序号 Td/s 21 1.498 6 1.497 2 1.499 7 1.496 3 1.498 8 1.495 4 1.498 9 1.493 5 1.497 10 1.493 序号 Td/s ..
由上表，可得均值Td?1.4964s
?Td?1.4964?10-5+0.001=1.014964?10-3s
?0?2?Td1??2??2?2??1.4964?1??0.01455508013??
?????4.199312323s?1??0??T??????d??????2?0T1?????d?-3222??1.014964?10??0.01455508013-4???2.705689144?10? ???2??1.4964???1??0.01455508013???6.782819534?10-4角频率的不确定度为：
2??0??0??0?0?4.204826965?6.782819534?10-4=2.848317766?10-3?0.0029s?1
?1角频率为：?0??4.1993?0.0029?s
???b?0.09146195424???0.06112132735Td1.496422??Td???b??????????T?d??b??1.014964?10-3??0.001700575??0.06112132735??????1.4964????0.09146195424? ?1.136816041?10?3????61.1?1.2??10?322??1???Td1.4964???16.36090123b?0.0914619542422??T?????????d???b??Td??b??1.014964?10-3??0.001700575??16.36090123?????? 1.49640.09146195424?????0.3043018822???16.36?0.31..
22Q?11??34.35226708?34.352?2?0.0145550801322?dQ?1??4??Q?????????2.705689144?10??0.6385849839?0.7 2d?2?0.01455508013?????Q?34.4?0.7（2）阻尼2
?n??10?I?int???int???5
?2??2?序号 1 2 3 4 5 ?（?） 163 144 127 113 100 yi?ln?i序号 6 7 8 9 10 ?（?） 88 78 68 60 53 yi?ln?i Di?yi?5?yi -0.616413386 -0.613104473 -0.624679381 -0.633043256 -0.634878272 -3.122118769 5.093750201 4.969813300 4.844187086 4.727387819 4.605170186 4.477336814 4.356708827 4.219507705 4.094344562 3.970291914 ?Di?1Ii D 11I1b?D?2?(yi?I?yi)?2IIi?1I5-0.624423754 ?(ln?i?1Ii?I?ln?i)
?1-3.122118769?(ln??ln?)???0.1248847508?i?5i225i?151I?b??(Di?D)2/(I?1)?15?(D?D)i2/(5?1)?0.001938944?0.0020
由b??2????2?1??0.5得到：
b2(?0.1248847508)2????0.01987210049 224π?b24?π?(?0.1248847508)2..
d?4?22???(?b)??b223/2db(4??b)?4?2223/2??4??(?0.1248847508)???3.084097451?10-4?3.1?10-4?0.001938944
这样，阻尼比为：??（1.987?0.031）?10-2序号 Td/s 1 1.500 6 1.497 2 1.499 7 1.497 3 4 1.490 9 1.494 5 1.498 10 1.492 1.487 8 1.495 序号 Td/s 由上表可得：Td?1.4949s
?Td?1.4949?10-5+0.001=1.014949?10-3s
?0?2?Td1??2??2?2??1.4949?1??0.01987210049??
?????4.203910824s?1??0??Td????????????2?0??Td??1??-3222??1.014949?10??0.01987210049-4???3.084097451?10? ???2??1.4949???1??0.01987210049???6.789687495?10-4角频率不确定度为：
2??0??0??0?0?4.203910824?6.789687495?10-4=2.854324075?10-3?0.0029s?1
?1角频率为：?0??4.2039?0.0029?s
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???b?0.1248847508???0.08354053836Td1.494922??T?????????d???b??Td??b??1.014949?10-3??0.001938944??0.08354053836?????? 1.4949?0.1248847508?????1.298278828?10?3????83.54?1.3??10?322??1???Td?11.97023648b22??Td???b??????????T?d??b??1.014949?10-3??0.001938944??11.97023648??????1.4949????0.1248847508? ?0.1860259091???11.97?0.19Q?11??25.16090336?25.162?2?0.019872100492222?dQ?1?-4??Q?????????3.084097451?10??0.3904905672?0.39 2?2?0.01987210049??d???Q?25.16?0.39 名称 下面将两个阻尼的部分振动参数的计算结果整理在表格中： 阻尼1 阻尼2 ? （1.456?0.027）?10-2（1.987?0.031）?10-2 ?0/s?14.1993?0.0029 4.2039?0.0029 ?/s?1 ?61.12?1.2??10?3 16.36?0.31 34.35?0.64 ?83.54?1.3??10?3 11.97?0.19 25.16?0.39 ?/sQ ..
二、受迫振动实验数据记录及处理 测定受迫振动的幅频特性和相频特性曲线
??4.288863691s?1 0由于实验中途更换仪器，现直接给出实验二的
表1阻尼1受迫振动振幅和相位关系对应表 ① 阻尼1 序号 1 2 3 4 5 6 7 8 9 10 11 12 13 T/s ?/? ?1/? 29.4 39.9 50.0 59.5 70.1 80.4 90.1 99.8 110.3 120.2 129.3 140.2 150.0 ?2/? 29.4 39.9 50.0 59.4 70.0 80.4 90.1 99.9 110.3 120.0 129.4 140.4 149.9 ?/? ?=2?/s T??0 1.514 1.499 1.488 1.482 1.474 1.469 1.465 1.460 1.455 1.449 1.443 1.443 1.419 58 73 86 97 106 110 112 109 102 94 83 68 52 29.4 39.9 50.0 59.45 70.05 80.4 90.1 99.85 110.3 120.1 129.35 140.3 149.95 4.150056346 0.967635403 4.191584595 0.977318212 4.222570771 0.984543011 4.239666199 0.988529015 4.262676599 0.993894165 4.277185369 0.997277059 4.288863691 1.000000000 4.30355158 1.003424657 4.318340417 1.006872852 4.336221744 1.011042098 4.354251772 1.015246015 4.354251772 1.015246015 4.427896622 1.032417195 ②阻尼2
表2阻尼2受迫振动振幅和相位关系对应表 序号 T/s ?/? ?1/? ?2/? ?/? ?=2?/s T??0 ..
1 2 3 4 5 6 7 8 9 10 11 12 13 1.529 1.509 1.495 1.487 1.478 1.472 1.466 1.459 1.453 1.446 1.436 1.424 1.405 46 57 67 74 79 82 83 81 76 71 62 52 40 30.4 40.0 50.4 59.6 70.3 79.8 90.5 99.9 110.2 119.2 129.4 139.4 149.2 30.2 40.2 50.4 59.5 70.4 80.0 90.5 100.1 110.1 119.1 129.4 139.4 149.1 30.3 40.1 50.4 59.55 70.35 79.9 90.5 100 110.15 119.15 129.4 139.4 149.15 4.109342909 0.958142577 4.163807361 0.970841617 4.202799537 0.979933110 4.225410429 0.985205111 4.251140262 0.991204330 4.268468279 0.995244565 4.285938136 0.999317872 4.306501239 1.004112406 4.324284451 1.008258775 4.345218055 1.013139696 4.375477233 1.020244986 4.412349233 1.028792135 4.472024012 1.042704626 根据表1和表2的数据，借助MATLAB计算机仿真，得到受迫振动的幅频特性曲线如图1所示。同时，受迫振动的相频特性曲线如图2 所示。
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12011010090阻尼1阻尼2（1.000，112） 振幅/度8070605040 0.95(0.9993,83)1w/w01.05
图1受迫振动幅频特性曲线
160阻尼1阻尼2（1，90） 140120相位/度10080604020 0.950.960.970.980.991w/w01.011.021.031.041.05
图2受迫振动相频特性曲线
?1?1由图像得?0?4.288863691s?4.30s
，与前面相符。
下面逐点XX测相位差?与由?0?arctan2??算值的相对偏差。
?02??2..
?1①阻尼1 ??0.06112132735,?0?4.288863691s
表3阻尼1误差与参数关系表 序号 ?/? ?=2?/s T?0?arctan2???02??2 E??0?? ?01 2 3 4 5 6 7 8 9 10 11 12 13 29.4 39.9 50.0 59.45 70.05 80.4 90.1 99.85 110.3 120.1 129.35 140.3 149.95 4.150056346 4.191584595 4.222570771 4.239666199 4.262676599 4.277185369 4.288863691 4.303551580 4.318340417 4.336221744 4.354251772 4.354251772 4.427896622 23.41692 31.84448 42.45252 51.00687 66.74388 79.16857 90.00000 103.4902 115.6699 127.6175 136.7162 136.7162 155.9330 -0.255502432 -0.252964407 -0.177786383 -0.165529271 -0.049534429 -0.015554531 -0.001111111 0.035174345 0.046424351 0.058906498 0.053879496 -0.026213426 0.038369043 ?1②阻尼2 ?=0.08354053836,?0?4.288863691s
表四阻尼2误差与参数关系表 序号 ?/? ?=2?/s T?0?arctan2???02??2 E??0?? ?01 2 3 30.3 40.1 50.4 4.109342909 4.163807361 4.202799537 24.48479 33.35051 43.85588 -0.237502956 -0.202480413 -0.149218759 ..
4 5 6 7 8 9 10 11 12 13 59.55 70.35 79.9 90.5 100 110.15 119.15 129.4 139.4 149.15 4.225410429 4.251140262 4.268468279 4.285938136 4.306501239 4.324284451 4.345218055 4.375477233 4.412349233 4.472024012 52.57484 65.60277 76.24877 87.99366 101.8978 112.8923 123.83 135.7498 145.5451 155.0306 -0.132671065 -0.072363255 -0.047885756 -0.028483188 0.018624543 0.024291294 0.037793749 0.04677576 0.042221277 0.037931866 附：原始数据记录表格
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清华大学物理实验A1阻尼振动及受迫振动实验报告 - 图文
