The displacement of particle in S.H.M. is x = A cos ( ω t + π /6 ) . Its speed will be maximum at time ( Sin 9 0 ∘ = 1 )

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The displacement of the particle is given by $x = A cos (ω t + π /6)$ .

The velocity of the particle is $v = \frac{d x}{d t} = - A ω sin (ω t + π /6)$ .

The speed of the particle is maximum when the magnitude of velocity is maximum, which occurs when $∣ sin (ω t + π /6) ∣ = 1$ .

For the first maximum speed, we have:

$ω t + \frac{π}{6} = \frac{π}{2}$

$ω t = \frac{π}{2} - \frac{π}{6}$

$ω t = \frac{π}{3}$

$t = \frac{π}{3 ω}$

Answer: $\frac{π}{3 ω} s$

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