A point performs simple harmonic oscillation of period T and the equation of motion is given by =a sin ( ωt+ /6 ) . After the elapse of what fraction of the time period the velocity of the point will…

Question

A point performs simple harmonic oscillation of period T and the equation of motion is given by =a sin ( ωt+ /6 ) . After the elapse of what fraction of the time period the velocity of the point will be equal to halfofits maximum velocity?

Accepted Answer

Correct answer: B. (b) x=a sin( ωt+ 6) dx dt= aω cos ( ωt+ /6 ) Max. velocity = aω aω2= aω cos ( ωt+ /6 ) ; cos ( ωt+ /6 )= 12 ⇒60^o or 2 6 radian = 2 T t+ /6 ⇒ 2 T t= 2 6- 6=+ 6 t=+ 6 T2 =(+ T12)

$A point performs simple harmonic oscillation of period and the equation of motion is given by . After the elapse of what fraction of the time period the velocity of the point will be equal to halfofits maximum velocity?$

Solution

More Wave Motion & Waves on String PYQs