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16.1.2017 4.1 Simple harmonic motion 1a.[4marks] Thisquestionisaboutsimpleharmonicmotion(SHM). Thegraphshowsthevariationwithtime oftheacceleration ofanobjectXundergoingsimple harmonicmotion(SHM). DeterminethemaximumdisplacementofX.Giveyouranswertoanappropriatenumberofsignificant figures. 1 1b.[2marks] AsecondobjectYoscillateswiththesamefrequencyasXbutwithaphasedifferenceof .Sketch, usingthegraphopposite,howtheaccelerationofobjectYvarieswith . 2.[1mark] Anobjectperformssimpleharmonicmotion(SHM)aboutacentralpoint.Theobjecthasvelocityvand accelerationawhenithasdisplacementxfromthepoint. Whichratioisconstant? B. C. D. 3.[1mark] AliquidinaU-tubeisgivenaninitialdisplacementandallowedtooscillate.Themotionoftheliquidis recordedusingamotionsensor.Whichgraphshowsthevariationwithtimetofthevelocityvofthe liquid? 2 4.[1mark] Abodyundergoessimpleharmonicmotion.Whichgraphcorrectlyshowsthevariationwith displacementxofthevelocityvofthebody? 5.[1mark] Thediagramshowsthevariationofvelocityvwithtimetforanobjectperformingsimpleharmonic motion. Whichofthefollowingshowshowtheaccelerationavarieswitht? 3 6.[1mark] Forabodyundergoingsimpleharmonicmotionthevelocityandaccelerationare A.alwaysinthesamedirection. B.alwaysinoppositedirections. C.inthesamedirectionforaquarteroftheperiod. D.inthesamedirectionforhalftheperiod. 7.[1mark] ApendulumswingsbackandforthinacirculararcbetweenXandY. Thependulumbobis A.alwaysinequilibrium. B.onlyinequilibriumatXandY. C.inequilibriumasitpassesthroughthecentralposition. D.neverinequilibrium. 8.[1mark] 4 ThegraphshowsmeasurementsoftheheighthofsealevelatdifferenttimestintheBayofFundy. Whichofthefollowinggivestheapproximateamplitudeandperiodofthetides? 9.[1mark] Thediagramsshowthevariationwithtimetofthedisplacementyofaparticleofamediumthrough whichawavetravels.WhichdiagramcorrectlyshowstheperiodTandamplitudeAofthewave? 5 10a.[2marks] Thisquestionisaboutsimpleharmonicmotion. Anobjectofmassmisplacedonafrictionlesssurfaceandattachedtoalighthorizontalspring.The otherendofthespringisfixed. TheequilibriumpositionisatB.ThedirectionBtoCistakentobepositive.Theobjectisreleasedfrom positionAandexecutessimpleharmonicmotionbetweenpositionsAandC. Definesimpleharmonicmotion. 10b.[3marks] (i)Ontheaxesbelow,sketchagraphtoshowhowtheaccelerationofthemassvarieswith displacementfromtheequilibriumpositionB. 6 (ii)Onyourgraph,labelthepointsthatcorrespondtothepositionsA,BandC. 10c.[3marks] (i)Ontheaxesbelow,sketchagraphtoshowhowthevelocityofthemassvarieswithtimefromthe momentofreleasefromAuntilthemassreturnstoAforthefirsttime. 7 (ii)Onyourgraph,labelthepointsthatcorrespondtothepositionsA,BandC. 10d.[3marks] Theperiodofoscillationis0.20sandthedistancefromAtoBis0.040m.Determinethemaximum speedofthemass. 11.[1mark] Thegraphshowshowthedisplacementvarieswithtimeforanobjectundergoingsimpleharmonic motion. Whichgraphshowshowtheobject’saccelerationavarieswithtimet? 8 12.[1mark] Whichgraphcorrectlyshowshowtheacceleration, ofaparticleundergoingSHMvarieswithits displacement, fromitsequilibriumposition? 13.[1mark] Thegraphshowshowthevelocity ofanobjectundergoingsimpleharmonicmotionvarieswithtime foronecompleteperiodofoscillation. Whichofthefollowingsketchgraphsbestshowshowthetotalenergy oftheobjectvarieswith ? 9 14.[1mark] Whichofthefollowinggraphsshowsthevariationwithdisplacement ofthespeed ofaparticle performingsimpleharmonicmotion. 15.[1mark] Thisquestionisaboutsimpleharmonicmotion(SHM). Thegraphshowsthevariationwithtime oftheacceleration ofanobjectXundergoingsimple harmonicmotion(SHM). Xhasamassof0.28kg.CalculatethemaximumforceactingonX. 10 17.[1mark] Aparticleperformssimpleharmonicoscillations.Whichofthefollowingquantitieswillbeunaffected byareductionintheamplitudeofoscillations? A.Thetotalenergy B.Themaximumspeed C.Themaximumacceleration D.Theperiod PrintedforJyvaskylanLyseonlukio ©InternationalBaccalaureateOrganization2017 InternationalBaccalaureate®-BaccalauréatInternational®-BachilleratoInternacional® 11