測(cè)G和牛頓反平方檢驗(yàn)實(shí)驗(yàn)中的數(shù)學(xué)建模.pdf

1、華中科技大學(xué)碩士學(xué)位論文測(cè)G和牛頓反平方檢驗(yàn)實(shí)驗(yàn)中的數(shù)學(xué)建模姓名：張雅婷申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：理論物理指導(dǎo)教師：羅俊邵成剛20090530II華中科技大學(xué)碩士學(xué)位論文AbstractGravitationalinteractionistheweakestamongthefourfundamentalinteractions.Asahighsensitivitytoolfdetectingweakfcethetsionpendulumh

2、asbeenwidelyusedingravitationalexperimentsinlabaty.Ingeneralthetqueactingonthetsionpendulumiscloselyrelatedtogeometricalrelatedparametersofthependulum.Therefeindertoobtainapreciseconfidentialexperimentalresultitisnecessa

3、rytocarefullyevaluatetheuncertaintiescontributedbyallrelatedparameters.Inthisthesisgeometricalparametersofthreeexperimentswereanalyzedindetailbasedontheexperimentalprinciplesdesigns.Intheexperiment“Theprecisionmeasuremen

4、tofNewtoniangravitationalconstantGwiththetimeofswingmethoddoublesphericalsourcemasses”ananalyticalexpressionofGwasderivedwithconsideringtheanelasticityofthetungstenfibercouplingofthemagicdamperthependulumthegeometricalpa

5、rameteruncertaintiesincludingtheflatnessverticalityofthependulumthemasscenteroffsetfmthegeometriccenterofthesourcemasseswereestimated.ThenweconcludethattheuncertaintyofthegravitationalconstantGcausedbygeometricalparamete

6、rsisabout11ppm.Intheexperiment“Theprecisionmeasurementofanelasticityeffectwithtwofiberstwopendulums”weestablishedamathematicalmodelinthisthesistofindoutvariationoffiber’sspringconstantbasedontwoslightlydifferentfrequenci

7、esmakingcrespondingcrectionfthevalueofG.Additionallyintheexperiment“TestofNewtonianInverseSquareLawatsubmillimetrerange”thegravitationaltqueactingonthependulumwasmathematicallymodeled.Thenwecalculatedthevariationofthegra

8、vitationaltqueintheprocessofchangingthedistancebetweensourcemasstestmassofthependulumfrom120μmto240μm.Finallytheexperimentalresultshowsthattheprimarydesignofthesourcemasspendulumensuresthevariationofthegravitationaltques