A mass attached to a spring performs S.H.M. whose displacement is x = 3 × 10⁻³cos 2π t m. The time taken to obtain maximum speed for the first time is (in s) (a) 1 (b) 1/2 (c) 1/4 (d) 1/8

Answer: (c). ω = 2π, so T = 1 s. x = Acos 2π t starts at the extreme position ( x = A) at t = 0. Speed is maximum at the mean position, reached after T/4 = 1/4 s. So the answer is (c) 1/4.

A mass attached to a spring performs S.H.M. whose displacement is x =… | MHT CET 2026 (11 Apr, Shift 2)

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Periodic Motion & SHM Basics

A mass attached to a spring performs S.H.M. whose displacement is $x = 3 \times 10^{-3}\cos 2\pi t$ m. The time taken to obtain maximum speed for the first time is (in s)

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Answer: (c)

$\omega = 2\pi$ , so $T = 1\ \text{s}$ .
$x = A\cos 2\pi t$ starts at the extreme position ( $x = A$ ) at $t = 0$ .
Speed is maximum at the mean position, reached after $\frac{T}{4} = \frac{1}{4}\ \text{s}$ .
So the answer is (c) $\frac{1}{4}$ .

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