The displacement of a particle executing SHM is given by x=10 (w t+(π)/(3)) m . The time period of motion is 3.14 ~s . The velocity of the particle at t=0 is ______ m / s .

Correct answer: 0 Given, aligned & T=3.14=(2 π)/(ω) & ω=2 rad / s & x=10 (ω t+(π)/(3)) & v= dx dt =10 ω (ω t+(π)/(3)) & at t=0 & v=10 ω ((π)/(3))=10 × 2 × (1)/(2)[using ω=2 rad / s] & v=10 m / s aligned

JEE Main 20244 AprilEvening Shift

Exam: JEE Main
Year: 2024
Date: 4 April
Shift: Evening Shift
Subject: Physics
Chapter: Oscillations

JEE Main 2024 · 4 April · Evening Shift · Physics · Oscillations

The displacement of a particle executing SHM is given by x=10 (w...

The displacement of a particle executing SHM is given by

x=10 \sin \left(w t+\frac{\pi}{3}\right) m

. The time period of motion is

3.14 \mathrm{~s}

. The velocity of the particle at

t=0

is ______

\mathrm{m} / \mathrm{s}

Correct answer

Step-by-step solution

Given,

\begin{aligned} & \mathrm{T}=3.14=\frac{2 \pi}{\omega} \\ & \omega=2 \mathrm{rad} / \mathrm{s} \\ & \mathrm{x}=10 \sin \left(\omega \mathrm{t}+\frac{\pi}{3}\right) \\ & \mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=10 \omega \cos \left(\omega \mathrm{t}+\frac{\pi}{3}\right) \\ & \text{ at } \mathrm{t}=0 \\ & \mathrm{v}=10 \omega \cos \left(\frac{\pi}{3}\right)=10 \times 2 \times \frac{1}{2}[\mathrm{using} \omega=2 \mathrm{rad} / \mathrm{s}] \\ & \mathrm{v}=10 \mathrm{ m} / \mathrm{s} \end{aligned}

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