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JEE Main 2021 (20 Jul, Shift 2) · Velocity & Acceleration in SHM

Velocity & Acceleration in SHM question from JEE Main 2021 (20 Jul, Shift 2)

Q60JEE Main 2021 · 20 JUL · SHIFT 2Medium

Velocity & Acceleration in SHM

A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 respectively. The time period of its oscillation is given as:

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Answer: (d)

$v_1^2 = \omega^2(A^2 - x_1^2)$ , $v_2^2 = \omega^2(A^2 - x_2^2)$ .
Subtract: $v_1^2 - v_2^2 = \omega^2(x_2^2 - x_1^2)$ .
$T = \frac{2\pi}{\omega} = 2\pi\sqrt{\frac{x_2^2 - x_1^2}{v_1^2 - v_2^2}}$ .
So the answer is (d).

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