Questions
Three simple harmonic motions in the same direction having the same amplitude a and same period are superposed. If each differs in phase from the next by 45o, then
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Correct option is C
Let simple harmonic motions be represented byy1=asinωt−π4;y2=asinωt and y3=asinωt+π4 Resultant will be y=asinωt−π4+sinωt+sinωt+π4=a2sinωtcosπ4+sinωt=a[2sinωt+sinωt]=a(1+2)sinωtResultant amplitude =(1+2)aEnergy is S.H.M. ∝( Amplitude )2∴EResultant ESingle =Aa2=(2+1)2=(3+22)⇒EResultant =(3+22)ESingleSimilar Questions
The displacement y of a particle executing periodic motion is given by . This expression may be considered to be a result of the superposition of ........... independent harmonic motions
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