The displacement of a particle executing SHM is given by x = 10sin (ω t + π/3) m. The time period of motion is 3.14 s. The velocity of the particle at t = 0 is _______ m/s. Numerical answer type. Work it out, then open the answer.

Answer: 10. ω = 2π/T = (2× 3.14)/(3.14) = 2 rad/s. v = dx/dt = 10ωcos (ω t + π/3). At t = 0: v = 10× 2×cos 60° = 10 m/s. Answer: 10 m/s.

The displacement of a particle executing SHM is given by x = 10sin (ω… | JEE Main 2024 (4 Apr, Shift 2)

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Velocity & Acceleration in SHM

The displacement of a particle executing SHM is given by $x = 10\sin\left(\omega t + \frac{\pi}{3}\right)\text{ m}$ . The time period of motion is $3.14\text{ s}$ . The velocity of the particle at $t = 0$ is _______ $\text{m/s}$ .

Numerical answer type. Work it out, then open the answer.

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Answer: 10

$\omega = \frac{2\pi}{T} = \frac{2\times 3.14}{3.14} = 2$ rad/s.
$v = \frac{dx}{dt} = 10\omega\cos(\omega t + \frac{\pi}{3})$ .
At $t = 0$ : $v = 10\times 2\times\cos 60^\circ = 10$ m/s.
Answer: 10 m/s.

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