MeasuretheYoung’,Low-frequencygenerator,,bothofitsendsdoesaslightlyvibration,themotionofitwillsatisfytheequation:∂4y∂x4+ρSEJ∂2y∂t2=0Where,ρisthedensityoftherod,Sisthecrosssectionoftherod,Jisthemomentofinertia,EistheYoung’,wecangetthat:1Xd4Xdx4=ρSEJ1Td2Tdt2And:yx,t=(B1chKx+B2shKx+B3cosKx+B4sinKx)Acos(ωt+φ)Where:ω=(K4EJρS)1/,,=-∂M∂x=-EJ∂3y∂x3=0M=EJ∂2y∂x2=0So:d3Xdx3x=0=0,d3Xdx3x=l=0,d2Xdx2x=0=0,d2Xdx2x=l=0Eliminatingtheequationsandusingthenumericalmethod,wecangettheKandlshouldsatisfyKl=0,,,,…Generally,hefrequencyasbasisfrequencywhenKl=,=,wegetthenaturalvibrationangularfrequencyis:ω=(()4EJρS)1/2AndgettheYoung’sModulus:E=×10-3ρl4SJω2=×10-2l3mJf2WherethemomentofinertiaJ=y2ds=πd464So:E=,listhelengthoftherod,disthediameter,misthemass,fistheresonancefrequencyofthesampl
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