清华大学物理实验A1阻尼振动与受迫振动实验报告.docx

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-.0序号yi =in q序号日% =1 nDi = yi425 - yi11294.859812404261104.700480366-0.15933203921284.852030264271094.691347882-0.16068238231274.844187086281084.682131227-0.16205585941274.84418708629108

2、4.682131227-0.16205585951254.828313737301074.672828834-0.15548490361254.828313737311064.663439094-0.16487464371244.820281566321064.663439094-0.15684247181234.812184355331044.644390899-0.16779345691224.804021045341034.634728988-0.169292057101214.795790546351034.634728988-0.161061557111214.79579054636

3、1024.624972813-0.170817732121204.787491743371024.624972813-0.162518929131194.779123493381014.615120517-0.164002976141184.770684624391004.605170186-0.165514438151174.762173935401004.605170186-0.157003749161184.77068462441994.59511985-0.175564774171174.76217393542984.584967479-0.177206456181164.753590

4、19143984.584967479-0.168622712191154.74493212844974.574710979-0.17022115201144.73619844845964.564348191-0.171850257211144.73619844846964.564348191-0.171850257221134.72738781947954.553876892-0.173510927231124.71849887148944.543294782-0.175204089241124.71849887149944.543294782-0.175204089251104.700480

5、36650934.532599493-0.167880873I工DiiA-4.166448636D-0.166657945于是得到：1 1 I 1b D 厂(yi I 一 yj (ln 弓 I ln 弓)I I i A I i =1252丄 a (In 3 25一1 n 弓)二-4166448636 =_6.666317818 10入+屆(Di D)2/(I 1)=25返2 -4(Dj - D) /(25 -1) = 2.565475395 1025 i总严二 -0.5由b=2二 -1 得至y：b2(-6.666317818 10 冷24冗2 b24 n2 (-6.666317818 10 冷

6、2= 1.060976836 10d ,)2db(“2心3/2亠(4 b )弟 2.565475395 10* 2 3 24- (-6.666317818 10 )= 4.083074011 10从而可得(1.061 _ 0.041) 10-3。序号12345T = 10Td /s14.92614.93514.94414.95114.958由上表，可得均值Td = 1.49428s。1.49428X 10-5 +0.001=1.014942810-3s 0二2心.讥 1= 2.49428 , 1 - 1.06 10_3 2= 4.204826965 s ：02+1.0149428心0_3 f1

7、.49428佃0976836 10 2 0.04 10_31 - 1.060976836 10 _4= 6.792186217 10也 3 1角频率的不确定度为 ：.0一 二 2.855996775 10_- 0.0029s0 -0由此，角频率为：0 二 4.2048-0.0029 s2、测量其他2种阻尼的相关振动参数。（1 ）阻尼1I 二 int int 5（2丿 12丿序号引=1 n q序号8QW = 1 n qDi = - yi11054.6539603506674.204692619-0.4492677312964.5643481917614.110873864-0.453474327

8、3884.4773368148564.025351691-0.4519851234804.3820266359503.912023005-0.4700036305734.29045944110463.828641396-0.461818045IZ Dii 4-2.286548856D-0.457309771一 1b D Q (% I yj Q (ln 如一In 可)I I i z! I i d1J “ 、-2.286548856 c c“一2二(In 耳 5 - InJ 2 .0914*5 i 5 ：b n1、 (Dj -D)2/(l -1)(Dj - D)2/(5-1) =0.0017005

9、75 ： 0.0017.2 -0.5由b - -2二 -1 得到:I 丫 5耳0.01455508013.0914*了2 2 324 b24:4 n2 (-0.09146195424)2T 4 2 2 32 0.0017005754兀2 +(0.09146195424 升= 2.705689144 10 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二1.4964s-5 -3Td =1.4964 10 +0.001=1.014

10、964 10 sd=4.199312323s*1.014964 0-31.4964J 0.01455508013(1 -(0.01455508013 f、2x2.705689144 0-44= 6.782819534 10角频率的不确定度为=4.204826965 6.782819534 10-4 =2.848317766 10- 0.0029sJ0 0角频率为：p 二 4.1993-0.0029 s.0914*0.06112132735Td1.4964= 0.061121327351.0149640-3 辽1.49642+ F 0.001700575.0914*=1.136816041 10

11、”-=61.11.2 101Tdb1.4964.0914*= 16.36090123=16.360901231.014964 00-3 1.496420.001700575.0914*= 0.3043018822.=16.36 _0.31Q 1 1 34.35226708 ： 34.352 2 0.0145550801312 0.0145550801322.705689144 10=0.6385849839 ： 0.7.Q =34.4 _0.7(2)阻尼2序号()W = Ind序号yi =l ndDi = y y11635.0937502016884.477336814-0.616413386

12、21444.9698133007784.356708827-0.61310447331274.8441870868684.219507705-0.62467938141134.7273878199604.094344562-0.63304325651004.60517018610533.97029191-0.6348782721 一 1 1b=D=送(y_yj=市送(ln q卡一I nQ)I I i 4 I i 4= (In 哥 - In 弓)=-3.1221218769 = _o.i2488475O85 i 4 5二 1(Di -D)2/(I -1)=5,(2Dj -D) /(5 -1) =

13、0.001938944 ： 0.0020(-0.12488475082 24 n2 (-0.1248847508)24 二2 _23/2(4 b )4二2 (-0.1248847508)20.001938944“ 2 丄5由b = -2慕汁 -1 得到：-0.019872100494 4=3.084097451 10 3.1 10这样，阻尼比为：(1.987 -0.031 ) 10-2序号12345T/s1.5001.4991.4871.4901.498序号678910Td/s1.4971.4971.4951.4941.492由上表可得：T； = 1.4949s_5 _3飞 T4949 10

14、+0.001=1.014949 10 s1.49491- 0.01987210049=4.203910824s ： -0彳01494910-3 %21.4949l，Z 0.01987210049, 0.01987210049 2-4肚3.08409745仆104= 6.789687495 10角频率不确定度为也閒=肌经=4.203910824 _币E= 0129.44.15005634623.41692-0.255502432239.94.19158459531.84448-0.252964407350.04.22257077142.45252-0.177786383459.454.23966

15、619951.00687-0.165529271570.054.26267659966.74388-0.049534429680.44.27718536979.16857-0.015554531790.14.28886369190.00000-0.001111111899.854.303551580103.49020.0351743459110.34.318340417115.66990.04642435110120.14.336221744127.61750.05890649811129.354.354251772136.71620.05387949612140.34.35425177213

16、6.7162-0.02621342613149.954.427896622155.93300.038369043阻尼 2 =0.08354053836 矶=4.288863691s表四阻尼2误差与参数关系表序号0/。2兀= /s T% =arctan 严 2o0 一蛍(p 币E= 0 %130.34.10934290924.48479-0.237502956240.14.16380736133.35051-0.202380413350.44.20279953743.85588-0.149218759459.554.22541042952.57484-0.132671065570.354.251

17、14026265.60277-0.072363255679.94.26846827976.24877-0.047885756790.54.28593813687.99366-0.02848318881004.306501239101.89780.0186245439110.154.324284451112.89230.02429129410119.154.345218055123.830.03779374911129.44.375477233135.74980.0467757612139.44.412349233145.54510.04222127713149.154.472018012155.03060.037931866附：原始数据记录表格