清華大學(xué)物理實(shí)驗(yàn)A1阻尼振動(dòng)與受迫振動(dòng)實(shí)驗(yàn)報(bào)告

1、 清華大學(xué)阻尼振動(dòng)與受迫振動(dòng)實(shí)驗(yàn)物理實(shí)驗(yàn)簡要報(bào)告班級(jí)姓名學(xué)號(hào)結(jié)稿日期：阻尼振動(dòng)與受迫振動(dòng)實(shí)驗(yàn)報(bào)告（簡要報(bào)告）一、阻尼振動(dòng)實(shí)驗(yàn)數(shù)據(jù)記錄及處理1、測量最小阻尼（阻尼0）時(shí)的阻尼比J和固有角頻率0I二int-=int(50=2512丿I2丿序號(hào)（。）y=In0ii序號(hào)0（。）y=In0iiD=y-yii+25i11294.859812404261104.700480366-0.15933203921284.852030264271094.691347882-0.16068238231274.844187086281084.682131227-0.16205585941274.844187086291

2、084.682131227-0.16205585951254.828313737301074.672828834-0.15548490361254.828313737311064.663439094-0.16487464371244.820281566321064.663439094-0.15684247181234.812184355331044.644390899-0.16779345691224.804021045341034.634728988-0.169292057101214.795790546351034.634728988-0.161061557111214.795790546

3、361024.624972813-0.170817732121204.787491743371024.624972813-0.162518929131194.779123493381014.615120517-0.164002976141184.770684624391004.605170186-0.165514438151174.762173935401004.605170186-0.157003749161184.77068462441994.59511985-0.175564774171174.76217393542984.584967479-0.177206456181164.7535

4、9019143984.584967479-0.168622712191154.74493212844974.574710979-0.17022115201144.73619844845964.564348191-0.171850257211144.73619844846964.564348191-0.171850257221134.72738781947954.553876892-0.173510927231124.71849887148944.543294782-0.175204089241124.71849887149944.543294782-0.175204089251104.7004

5、8036650934.532599493-0.167880873Dii=1-4.166448636D-0.166657945于是得到：b=D=工(y-y)=工(In0-In0)TOC o 1-5 h zI12i+1i12i+1ii=1i=11吝-4.166448636=x乙(In0-In0)=-6.666317818x10-3252i+25/252i=1A=1.E(D-D)2/(I-1)=丄E(D-D)2/(25-1)=2.565475395x10-4bIi25i由b=-2兀t-210.5得到：=1.060976836x10-3(-6.666317818x10-3)24xn2+(-6.6663

6、17818x10-3)2A=(dba)2db4兀2,A(4兀2+b2)3/2bx2.565475395x10-44兀2+(-6.666317818x10-3)23/2=4.083074011x10-5從而可得:=(1.061土0.041)x10-3。序號(hào)12345T=10F/sid14.92614.93514.94414.95114.958由上表可得均值Td=1.4942&。=1.49428x10-5+0.001=1.0149428x10-3sTd1.49428x0J1-G.06x10-3=4.204826965s-1P-a1.0149428x10-3)1.49428丿U-匚1.0609768

7、36x10-3八“x0.04x10-3.060976836x10-3丿=6.792186217x10-4匚丿A角頻率的不確定度為：A二氣二2.855996775x10-3=0.0029s-1%00由此，角頻率為：=（4.2048土0.0029）s-102、測量其他2種阻尼的相關(guān)振動(dòng)參數(shù)。1）阻尼1.(n)I=mt12丿(10)=intI2丿序號(hào)9（。）y=ln9ii序號(hào)9（。）y=ln9iiD=yyii+5i11054.6539603506674.204692619-0.4492677312964.5643481917614.110873864-0.4534743273884.47733681

8、48564.025351691-0.4519851234804.3820266359503.912023005-0.4700036305734.29045944110463.828641396-0.461818045Dii=1-2.286548856D-0.457309771b=D=工(y-y)=丄工(ln9-ln9)TOC o 1-5 h zI12i+1i12i+1ii=1i=11丫-2.286548856=x乙(ln9ln9)=-0.0914619542452i+5i52i=1A=1J工(DD)2/(I1)=5J工(DD)2/(51)=0.001700575沁0.0017由b=-2兀得到：

9、4xn2lZ49195424424)2=O014555080130=4兀2(4k2+b2b4k24k2+(-0.09146195424匕32x0.001700575=2.705689144x10-4可得阻尼比：0=(1.456土0.027)x10-2序號(hào)12345T/sd1.4981.4991.4981.4981.497序號(hào)678910T/sd1.4971.4961.4951.4931.493由上表可得均值Td=l4964sA=1.4964x10-5+0.001=1.0149640.5得到：4財(cái)和囂囂二=-19872100494兀2A(4兀2+b2)3/2bX0.0019389444兀2+(-

10、0.1248847508)23/2=3.084097451X10-4沁3.1x10-4這樣，阻尼比為：:=(1.987土0.031)x10-2序號(hào)12345T/sd1.5001.4991.4871.4901.498序號(hào)678910T/sd1.4971.4971.4951.4941.492由上表可得：Td=1.4949sA=1.4949x10-5+0.001=1.014949x10-3s0Td=2兀/1.4949x：1-(0.01987210049匕=4.203910824s-1Am0m0Td丿P-au-匚2匚丿1.014949X10-3)(0.019872100491.4949丿、7X3.08

11、4097451x10-4(1-(0.01987210049=6.789687495X10-4角頻率不確定度為：AA=mf=4.203910824x6.789687495x10-4=2.854324075x10-30.0029s-1m00m0角頻率為：m=(4.2039+0.0029)s-100.12488475081.4949=0.08354053836dAP卩=0.08354053836x1.014949x10-31.4949(0.001938944)2+(0.1248847508丿=1.298278828x10-3.卩=(83.54土1.3)x103t=1=Td=11.97023648卩b

12、=0.186025909111Q=:2=25.16090336沁25.162x0.01987210049T=11.97土0.19AQ1x3.084097451x10-4十2x0.019872100492丿Q=25.16土0.39=0.3904905672沁0.39面將兩個(gè)阻尼的部分振動(dòng)參數(shù)的計(jì)算結(jié)果整理在表格中：名稱阻尼1阻尼2(1.456土0.027)x10-2(1.987土0.031)x10-2o/s104.1993土0.00294.2039土0.00290/s-1(61.12土1.2)xl03(83.54土1.3)xl03T/s16.36土0.3111.97土0.19Q34.35土0.6

13、425.16土0.39二、受迫振動(dòng)實(shí)驗(yàn)數(shù)據(jù)記錄及處理測定受迫振動(dòng)的幅頻特性和相頻特性曲線由于實(shí)驗(yàn)中途更換儀器，現(xiàn)直接給出實(shí)驗(yàn)二的o二4.288863691sj阻尼1表1阻尼1受迫振動(dòng)振幅和相位關(guān)系對應(yīng)表序號(hào)T/s0/。申/。19/29/2兀,=/sT011.5145829.429.429.44.1500563460.96763540321.4997339.939.939.94.1915845950.97731821231.4888650.050.050.04.2225707710.98454301141.4829759.559.459.454.2396661990.98852901551.47

14、410670.170.070.054.2626765990.99389416561.46911080.480.480.44.2771853690.99727705971.46511290.190.190.14.2888636911.00000000081.46010999.899.999.854.303551581.00342465791.455102110.3110.3110.34.3183404171.006872852101.44994120.2120.0120.14.3362217441.011042098111.44383129.3129.4129.354.3542517721.01

15、5246015121.44368140.2140.4140.34.3542517721.015246015131.41952150.0149.9149.954.4278966221.032417195阻尼2表2阻尼2受迫振動(dòng)振幅和相位關(guān)系對應(yīng)表序號(hào)T/s0/9/19/29/2兀,=/sT011.5294630.430.230.34.1093429090.95814257721.5095740.040.240.14.1638073610.97084161731.4956750.450.450.44.2027995370.97993311041.4877459.659.559.554.225410

16、4290.98520511151.4787970.370.470.354.2511402620.99120433061.4728279.880.079.94.2684682790.99524456571.4668390.590.590.54.2859381360.99931787281.4598199.9100.11004.3065012391.00411240691.45376110.2110.1110.154.3242844511.008258775101.44671119.2119.1119.154.3452180551.013139696111.43662129.4129.4129.4

17、4.3754772331.020194986121.42452139.4139.4139.44.4123492331.028792135131.40540149.2149.1149.154.4720180121.042704626根據(jù)表1和表2的數(shù)據(jù)，借助MATLAB計(jì)算機(jī)仿真，得到受迫振動(dòng)的幅頻特性曲線如圖1所示。同時(shí)，受迫振動(dòng)的相頻特性曲線如圖2所示。w/w0圖1受迫振動(dòng)幅頻特性曲線度/位相0.950.960.970.980.9911.011.021.031.041.05w/w00800圖2受迫振動(dòng)相頻特性曲線由圖像得O0二4.288863691s-1-4.30s-1，與前面相符。2陽下面

18、逐點(diǎn)求實(shí)測相位差與由9二arctan算值的相對偏差。02一20阻尼10二0.06112132735=4.288863691s-1,0表3阻尼1誤差與參數(shù)關(guān)系表序號(hào)9/2兀/3=/sT2039二arctan032-320廠9-990129.4441692-0.255502432239.94.19158459531.84448-0.252964407350.04.22257077142.45252-0.177786383459.454.23966619951.00687-0.165529271570.054.26267659966.74388-0.049534429680.44.27718536979.16857-0.015554531790.14.28886369190.00000-0.001111111899.854.303551580103.49020.0351743459110.34.318340417115.66990.04642435110120.14.336221744127.61750.05890649811129.354.354251772136.71620.05387949612140.34.3542517721