1、清华大学物理实验A1阻尼振动与受迫振动实验报告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姓名学号结稿日期：阻尼振动与受迫振动实验报告（简要报告）、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 0n50int int 2522序号()yi ln i序号()yi ln iDi yi 25 yi11294.859812404261104.700480366-0.15933203921284.852030264271094.691347882-0.16068238231274.844187086281084.682131227-0.16205585941274.
2、844187086291084.682131227-0.16205585951254.828313737301074.672828834-0.15548490361254.828313737311064.663439094-0.16487464371244.820281566321064.663439094-0.15684247181234.812184355331044.644390899-0.16779345691224.804021045341034.634728988-0.169292057101214.795790546351034.634728988-0.1610615571112
3、14.795790546361024.624972813-0.170817732121204.787491743371024.624972813-0.162518929131194.779123493381014.615120517-0.164002976141184.770684624391004.605170186-0.165514438151174.762173935401004.605170186-0.157003749161184.77068462441994.59511985-0.175564774171174.76217393542984.584967479-0.17720645
4、6181164.75359019143984.584967479-0.168622712191154.74493212844974.574710979-0.17022115201144.73619844845964.564348191-0.171850257211144.73619844846964.564348191-0.171850257221134.72738781947954.553876892-0.173510927231124.71849887148944.543294782-0.175204089241124.71849887149944.543294782-0.17520408
5、9251104.70048036650934.532599493-0.167880873IDi i 1-4.166448636D-0.166657945于是得到:1251 IFi25(lni 1(yi i1i 25Inx)i)1 ，、2 (ln i I ln i )I i 1-4.1664486362526.666317818 10 * 3_2_ 4(Di D) /(25 1) 2.565475395 100.5得至1J：b24冗2 b2(6.666317818 10 3)23 2(6.666317818 10 )31.060976836 104(4224兀3/2 2.565475395 10
6、 42 _ _ 3 2 3/24 2 ( 6.666317818 10 3)2 _ _ 54.083074011 10序号12345T 10T7 /s14.92614.93514.94414.95114.958(1.061 0.041) 10-3。从而可得由上表，可得均值Td 1.49428s。5 31.49428 105+0.001=1.0149428 103s2 1.494281 1.06 10-3 24.204826965 s2TdTd1.060976836 10 -3角频率的不确定度为:0 0 2.855996775 10-3 0.0029s 10由此，角频率为:0 4.2048- 1
7、0.0029 s2、测量其他2种阻尼的相关振动参数。(1)阻尼1序号()yi ln i序号()yi ln iDi yi 5 yi11054.6539603506674.204692619-0.4492677312964.5643481917614.110873864-0.4534743273884.4773368148564.025351691-0.4519851234804.3820266359503.912023005-0.4700036305734.29045944110463.828641396-0.461818045IDii 1-2.286548856D-0.457309771Iin
8、t52, 1 1 ,b D 2 (x iI I i 11 5-2 (In i 5 ln5 i 1yji)72 (ln i II i 1-2.28654885652ln i).0914*1 , (Di D)2/(5 1) 0.0017005755 12 0.5由b 2 1 得至ij：4 2 b2 32 b2 2 3 24.0914*0.0017005752.70568914410可得阻尼比： (1.456 0.027) 10-2序号12345Td/s1.4981.4991.4981.4981.497序号678910Td/s1.4971.4961.4951.4931.493由上表，可得均值Td 1
9、.4964st 1.4964 10 +0.001=1.014964 10 sd2 1.4964 1 14.199312323s0.0145550801322.705689144 10-4_ _ -46.782819534 10角频率的不确定度为:0 4.2048269650 06.782819534 104=2.848317766 10-3 0.0029s 角频率为： 0 4.1993 0.0029 sb.0914*1.49640.0611213273520.001700575.0914*1.136816041 10 61.1 1.2 1030.304301882216.36 0.3134.4
10、 0.7(2)阻尼2n .I int - int2序号()yi ln i序号()yi ln iDi yi 5 yi11635.0937502016884.477336814-0.61641338621444.9698133007784.356708827-0.61310447331274.8441870868684.219507705-0.62467938141134.7273878199604.094344562-0.63304325651004.60517018610533.970291914-0.634878272IDii 1-3.122118769D-0.624423754I_ 2D)
11、 /(I 1)1 . (Di D)2/(5 1) 0.001938944 0.00205，0.51 得到:jb2( 0.1248847508)山兀2 b2 4 tt2 ( 0.1248847508:20.01987210049(4 2 b2)3/22 2 3/24 2 ( 0.1248847508)2b0.001938944_ _ _ -4 _ -43.084097451 10 3.1 10序号12345Td/s1.5001.4991.4871.4901.498序号678910Td/s1.4971.4971.4951.4941.492这样，阻尼比为： (1.987 0.031) 10-2由上表
12、可得：Td 1.4949s-5-3t 1.4949 10 +0.001=1.014949 10 s d0 2 / Td 12 1.4949 1 0.01987210049 2 14.203910824s2TdTd1.014949 10-31.49490.01987210049 2 3.084097451 10-41 0.01987210049- - -46.789687495 104角频率不确定度为:0 4.2039108240 04 3 16.789687495 104=2.854324075 103 0.0029s 1角频率为： 0 4.2039 0.0029 sbTT0.12488475
13、081.4949.0835*2TdTd1.298278828 10 383.54 1.3 10 30.186025909111.97 0.191 1Q 25.16090336 25.162 2 0.0198721004921 .42 3.084097451 1042 0.019872100492Q 25.16 0.39卜面将两个阻尼的部分振动参数的计算结果整理在表格中:名称阻尼1阻尼2(1.456 0.027) 10-2(1.987 0.031) 10-20/ s 14.1993 0.00294.2039 0.0029/ s 1361.12 1.2 10383.54 1.3 10/s16.36
14、 0.3111.97 0.19Q34.35 0.6425.16 0.39、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1由于实验中途更换仪器，现直接给出实验二的 0 4.288863691s阻尼1表1阻尼1受迫振动振幅和相位关系对应表序 号T/s/1 /2 /一/T011.5145829.429.429.44.1500563460.96763540321.4997339.939.939.94.1915845950.97731821231.4888650.050.050.04.2225707710.98454301141.4829759.559.459.454.23966619
15、90.98852901551.47410670.170.070.054.2626765990.99389416561.46911080.480.480.44.2771853690.99727705971.46511290.190.190.14.2888636911.00000000081.46010999.899.999.854.303551581.00342465791.455102110.3110.3110.34.3183404171.006872852101.44994120.2120.0120.14.3362217441.011042098111.44383129.3129.4129.
16、354.3542517721.015246015121.44368140.2140.4140.34.3542517721.015246015131.41952150.0149.9149.954.4278966221.032417195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 /一/3/sT011.5294630.430.230.34.1093429090.95814257721.5095740.040.240.14.1638073610.97084161731.4956750.450.450.44.2027995370.97993311041.4877459.659.55
17、9.554.2254104290.98520511151.4787970.370.470.354.2511402620.99120433061.4728279.880.079.94.2684682790.99524456571.4668390.590.590.54.2859381360.99931787281.4598199.9100.11004.3065012391.00411240691.45376110.2110.1110.154.3242844511.008258775101.44671119.2119.1119.154.3452180551.013139696111.43662129
18、.4129.4129.44.3754772331.020194986121.42452139.4139.4139.44.4123492331.028792135131.40540149.2149.1149.154.4720180121.042704626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。120图1受迫振动幅频特性曲线图2受迫振动相频特性曲线由图像得0 4.288863691S 1 4.30S 1与前面相符。2卜面逐点求头测相位差 与由0 arctan 2算值的相对偏差。0阻尼 1 0.061121
19、32735 0 4.288863691s表3阻尼1误差与参数关系表序号一/2/sT-20 arctan 2 20E -00129.44.15005634623.41692-0.255502432239.94.19158459531.84448-0.252964407350.04.22257077142.45252-0.177786383459.454.23966619951.00687-0.165529271570.054.26267659966.74388-0.049534429680.44.27718536979.16857-0.015554531790.14.28886369190.00
20、000-0.001111111899.854.303551580103.49020.0351743459110.34.318340417115.66990.04642435110120.14.336221744127.61750.05890649811129.354.354251772136.71620.05387949612140.34.354251772136.7162-0.02621342613149.954.427896622155.93300.038369043阻尼 2 .0835* 0 4.288863691s表四阻尼2误差与参数关系表序号一/= T-20 arctan 2 20E
21、 0130.34.10934290924.48479-0.237502956240.14.16380736133.35051-0.202380413350.44.20279953743.85588-0.149218759459.554.22541042952.57484-0.132671065570.354.25114026265.60277-0.072363255679.94.26846827976.24877-0.047885756790.54.28593813687.99366-0.02848318881004.306501239101.89780.0186245439110.154.324284451112.89230.02429129410119.154.345218055123.830.03779374911129.44.375477233135.74980.0467757612139.44.412349233145.54510.04222127713149.154.472018012155.03060.037931866附：原始数据记录表格 2 0.04 1031 1.060976836 10 -46.792186217 100.01455508013
