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# Pendulum experiment

## Purposeoftheexperiment

1.Useasimplependulumtomeasurethelocalaccelerationofgravity.

2.Studytheperiodofsimplependulumvibration.

3.Practiceusingmeterrulerandstopwatch.

## Instruments

Singlependulum,meterruler,stopwatch(ordigitalmillisecondmeter),verniercaliper.

## Experimentalprinciple

(Figure1),whereisthelocalgravitationalacceleration,whichisthelinearaccelerationofthehammeratthistime.Supposethelengthofasimplependulumis,thentheangularaccelerationofthependulumisequalto,thatis

(1)Whenthependulumangleisverysmall(usually5°),itcanbeconsideredthatatthistime

(2)Thatis,theangularaccelerationofvibrationisproportionaltotheangulardisplacement.Thenegativesignintheformulameansthatthedirectionsofangularaccelerationandangulardisplacementarealwaysopposite.Atthistime,thevibrationofasimplependulumisasimpleharmonicvibration.Fromtheoreticalanalysis,itisknownthattherelationshipbetweenitsvibrationperiodandtheabove-mentionedproportionalcoefficientis,so

(3)isthependulumlength,thedistancebetweentheweightofthependulumandthesuspensionpoint,andthelocalgravityAcceleration.Transformequation(3)toget

(4)Substitutingthemeasuredpendulumlengthandcorrespondingperiodintotheaboveequationtoobtainthelocalgravityaccelerationvalue.Thisformulacanberewrittenas

(5)Thismeansthatthereisalinearrelationshipbetweenand,andisitsslope.Ifthecorrespondingperiodismeasuredforvariouspendulumlengths,theslopeofthegraphcanbeFindthevalue.Therelationshipbetweentheoscillationperiodofthependulumandtheangleofthependulumcanbederivedtheoreticallytoobtaintheperiodwhenitis0°.Ifyouomitandthefollowingitems,then

(6)Iftheperiodofdifferentswinganglesismeasured,thisformulacanbetestedbydrawingaline.

## Experimentalcontent

Useastopwatchtomeasurethetimeofasinglependulumswingingcontinuouslyfor50cycles,measuring6times.Notethattheswingangleshouldbelessthan10°.

Whenusingthestopwatchtomeasurethecycle,youshouldpressthestopwatchandcount"0"whenthependulumpassesthebalanceposition.Whenacycleiscompleted

"1",andthencontinuetoEverytimeacycleiscompleted,count2,3,...,andfinally,stopthewatchwhilecountingthe50th.

3.Usethedatafromstep1tofinditserror.

4.Usethedatafromsteps1and2toplotthelineandfindtheslopeandvalueoftheline.

5.Usethedatainstep3todrawthegraphline,andfromtheinterceptandslopeofthegraphline,checkwhetherthe

coefficientinequation(6)isequalto.

## Mattersneedingattention

1.Tightenthemainspringbeforeusingthestopwatch,butdonotovertightenit,soasnottodamagethemainspring.

2.Donotuseexcessiveforcewhenpressingthetabletopreventdamagetotheparts.