A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin( ω t + π /6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity? (a) T/3 (b) T/12 (c) T/8 (d) T/6

Answer: (b). v = aωcos (ω t + π/6), vmax = aω. v = vmax2 ⇒ cos (ω t + π/6) = 1/2 ⇒ ω t + π/6 = π/3 ω t = π/6 ⇒ 2π/Tt = π/6 ⇒ t = T/12 So the answer is (b) T/12.

A point performs simple harmonic oscillation of period T and the… | NEET 2008 (AIPMT)

Q34NEET 2008 · AIPMTEasy

Wave Basics & Properties of Sound

A point performs simple harmonic oscillation of period T and the equation of motion is given by x = a sin( $\omega$ t + $\pi$ /6). After the elapse of what fraction of the time period the velocity of the point will be equal to half of its maximum velocity?

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Answer: (b)

$v = a\omega\cos(\omega t + \frac{\pi}{6})$ , $v_{max} = a\omega$ .
$v = \frac{v_{max}}{2} \Rightarrow \cos(\omega t + \frac{\pi}{6}) = \frac{1}{2} \Rightarrow \omega t + \frac{\pi}{6} = \frac{\pi}{3}$
$\omega t = \frac{\pi}{6} \Rightarrow \frac{2\pi}{T}t = \frac{\pi}{6} \Rightarrow t = \frac{T}{12}$
So the answer is (b) $T/12$ .

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