SIMPLEHARMONICMOTION

1. Thepistonofsteamenginemoveswithsimpleharmonicmotion.Thecrankrotate3sat120rpmandthestrokelengthis2metres.Findthevelocityandaccelerationofthepiston,whenitisatadistanceof0.75metrefromthecentre.Ans:a=118.4m/s2

2. Abodymovingwithsimpleharmonicmotion,hasanamplitudeof1meterandtheperiodofcompleteoscillationis2seconds.Whatwillbethevelocityandaccelerationofthebodyafter0.4secondfromtheextremeposition?Ans:a=9.38m/s2

3. Findamplitudeandtimeperiodofaparticlemovingwithsimpleharmonicmotion,whichhasavelocityof9m/satthedistanceof2mand3mrespectivelyfromthecentre.Ans:t=1.75s

4. Inssystemtheamplitudeofthemotionis5mandthetimeis4seconds.Findthetimerequiredbytheparticleinpassingbetweenpointswhichareatdistancesof4mand2mfromthecentreofforceandareonthesamesideofit.Ans:t=0.33s

5. Abodyperformingsimpleharmonicmotionhasavelocityof12m/swhenthedisplacementis50mm,and3m/swhenthedisplacementis100mm,thedisplacementbeingmeasuredfromthemid-point.Calculatethefrequencyandamplitudeofthemotion.Whatistheaccelerationwhenthedisplacementis75mm?Ans:a=1332.6m/s2

6. Aparticlemovingwithsimpleharmonicmotionhasanaccelerationof6m/s2atadistanceof1.5mfromthecentreofoscillation.Findthetimeperiodoftheoscillation.Ans:a=1332.6m/s2

7. Abodyweighing150Nmoveswithsimpleharmonicmotion.Thevelocityandaccelerationofthebodywhenitis200mmfromthecentreofoscillationare5m/sand20m/s2respectively.Determine(a)amplitudeofmotionand,(b)no.ofvibrationsperminute.Ans:539mm,95.5

8. Aparticlemoveswithsimpleharmonicmotion.Wentheparticleis0.75mfromthemid-path,itsvelocityis11m/sandwhen2mfromthemid-pathitsvelocityis3m/s.Findtheangularvelocity,periodictimeanditsmaximumacceleration.Ans:a=1332.6m/s2

9. Aparticlemovingwithsimpleharmonicmotion,hasavelocityof20m/satitscentralposition.Iftheparticlemakestwooscillationspersecond,find(i)amplitudeofmotionand(ii)velocityat1/4thdistanceoftheamplitude.Ans1.59m,19.35m/s