A mass attached to a spring performs S.H.M. whose displacement is x = 3 × 1 0 − 3 cos 2 π t metre. The time taken to obtain maximum speed for the first time is

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The displacement of the particle is given by $x = 3 \times 1 0^{- 3} cos (2 π t)$ .

Velocity is the rate of change of displacement, $v = \frac{d x}{d t} = - 3 \times 1 0^{- 3} \times 2 π sin (2 π t)$ .

The speed is maximum when the particle passes through the mean position, which corresponds to $∣ sin (2 π t) ∣ = 1$ .

For the first time, this occurs when $2 π t = \frac{π}{2}$ .

$t = \frac{1}{4}$ s.

Answer: $\frac{1}{4} s$

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