DSHSAPPhysics Chapter13HarmonicMotion
FormalLab
Lab#14SimpleHarmonicMotionExploration
Theory:Allitemsthatundergosimpleharmonicmotionexhibitsimilarcharacteristics.Forinstance,ifaneverchangingnetforce
providesthebasisforharmonicmotion(pendulumorHookeaninnature),theposition,velocity,andaccelerationgraphswillall
conformtopredictablesinwaves.Thesewavescanbeanalysedanddatacanbeconstructed.
Forexample,considerthefollowingpendulummomentandthegraphsthatarecreatedforeachpositionofthependulumbelow:
AsthependulumstartsatA1andmovestoB2,ThevelocityatA1is–vmax,itspositionis0(fromequilibrium)anditsaccelerationis
0(netforceequalszero).Ifweplotthep-v-aforallthestepsofthependulumswingingachartsuchasfigure1andagraphsuchas
figure2willberealized.
B
D
2
A -C -E
3
1
FIGURE1
FIGURE2
4
5
Theironyofthischartandgraphisthattheywouldbeidenticaltotheone’sproducedbythefollowingscenarioofablock–springsystemoscillatingonafrictionless
tableasshownbelow:
Objective:toexplorethephenomenaofsimpleharmonicmotion(SHM)asdemonstratedinapendulumsystemandspringsystem.
Specifically,wewillgraphthedependenceofposition,velocity,andaccelerationasfunctionsoftime.
materials:
equations
motionsensor f=cyc/sf=1/T
masses slinkyspringonplate
1. OpenupDataStudioonthecomputerandpluginthemotionsensor.SelectCreateanExperiment.Next,clickthe“Set
Up”iconandclickposition,velocity,andacceleration.Nowdragallthreeiconsontheleft,downthescreenand
placethemintothegraphicon.Thiswillsetuponegraphwiththep-v-aalldisplayedtogether.
2. Mountarodsoitisvertical.Attachthependulumclamptotherodnearthetopandsuspendabrassmass(yourchoice)
withonestringsasshownbelowinfigure1.Next,placetheMotionSensornexttothependulumbobasshowninFigure
2.Alignthesensorsothebrasscoloreddiskisverticalandfacingthebobandisaimedalongthedirectionthatthe
pendulumwillswing.
Fig1
Fig2
*Setsensoronpersonmode
3.
4.
5.
Measureandrecordthemassmofthefirstpendulumbob.Putthefirstpendulumbobatthemiddleofthelongpieceofstring.
MeasureandrecordthelengthLofthependulumfromthebottomedgeofthependulumclamptothemiddleofthefirstpendulum
bob(seeFigure1).
Adjustthependulumclampupordownsothatthependulumbobisdirectlycenteredinfrontofthebrasscoloreddiskonthefront
ofthesensor.Nowslidethesensorawayfromthehangingpendulumbobabout25cm(10in).
RecordData:ChangingMass
6.Pullthependulumbobbackabout10cmandletitgo.Allowthependulumtoswingbackandforthaboutfivetimestosmoothits
motionout.
7.Press“Start”tostartrecordingdata.
Aftertenseconds,press“Stop”tostoprecording.
8.Forasecondrun,removethefirstpendulumbob.Measureandrecordthemassofasecondpendulumbobandputitonthestring.Remeasurethependulumlengthandadjustthestringsothelengthisthesameasforthefirstpendulumbob.
9.Repeatthedatarecordingprocedure.
Donoerasethepreviousrun,keepitonthesamegraph!
10.Measureandrecordthemassofathirdpendulumbobandputitonthestringinplaceofthesecondpendulumbob.Repeatthedata
recordingprocess.
Atthispointtakeascreenshotofyoudata(shift+command+4),andprintusingMicrosoftWord.
RecordData:ChangingLength
11.Putthefirstpendulumbobbackonthestring.Adjustthependulumclampandthestringsothelengthofthependulumis10cm
shorterthantheoriginallength.Recordthenew,shorterpendulumlength.
12.Performthesamedatarecordingprocedure.
13.Foranotherrun,shortenthelengthanother10cm.Recordthenewpendulumlengthandrepeatthedatarecordingprocedure.
14.Atthispointtakeascreenshotofyoudata(shift+command+4),andprintusingMicrosoftWord.
Analysis
1.Readbothgraphstodeterminetheperiodofthependulum’sswingforeachtrial.Recordindatatable.
2.Onthegraph,identifythecrest,amplitudeandwavelengthusingaredpenciltomarktheseaspects.
Questions
1.Whatistheshapeofthegraphofpositionversustimeforthependulum?
2. Whathappenedtoyourmeasuredvaluesfortheperiodwhenyouchangedthemassofthependulumbob?
3. Whathappenedtoyourmeasuredvaluesfortheperiodwhenyouchangedthelengthofthependulum?
4.ReferencetheChangingLengthportionofthislab.Calculatetheperiodagainusingtheequation
.
5.DoapercentageoferrorfromAnalysisquestion#2.
PartIIMassonaslinky
Removethependulumfromtheringstandandreplaceitwitharingstandanda100gmass.Allowtheplatetooscillateupanddownabovethe
motionsensor.Youmayneedtoputsensoronfloortohaveenoughroomforthis!Makesureitis40cmawayfromthesensorfaceoryourdata
willbeskewed.
1.Pulltheplatedownabout10cmandletitgo.Allowtheplatetogoupanddownandabout2timestosmoothitsmotionout.
Be
suretorecordthemassofthisfirst100gmass.
7.Press“Start”tostartrecordingdata.
Afterfiveseconds,press“Stop”tostoprecording.
8.Forasecondrun,place100gmoreontotheplate(tapeit).Measureandrecordthemassofasecondtrialandputitonthedatatable.
9.Repeatthedatarecordingprocedure.
Donoerasethepreviousrun,keepitonthesamegraph!
10.Measureandrecordthemassofathird100gmassandputitonthestand.Repeatthedatarecordingprocess.
Atthispointtakeascreenshotofyoudata(shift+command+4),andprintusingMicrosoftWord.
Questions
1.Readallgraphstodeterminetheperiodofthespring’soscillationforeachtrial.Recordindatatable.
2.Nowusetheequation
a.
3.
Ingeneral,aretheysimilar?
Accordingtotheequation
Conclusion
Writeyourconclusionnow!
andcalculatethetheoreticalperiodsoftheplatesystem.
whatisthevelocityoftheplateasitpassesthroughtheequilibriumposition