Oscillations - Result Question 43

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

(a) T/8

(b) T/6

(c) T/3

(d) T/12

[2008]

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Answer:

Correct Answer: 47. (d)

Solution:

  1. (d) We have x=asin(ωt+π6)

Velocity, v=dxdt=aωcos(ωt+π6)

Maximum velocity =aω

According to question,

aω2=aωcos(ωt+π6)

or, cos(ωt+π6)=12=cos60 or cosp3

wt+p6=p3

wt=p3p6 or, wt=p6 or, 2pTt=p6t=T12



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