Kelvi

A particle is executing SHM along a straight line. Its velocities at distances $x_1$ and $x_2$ from the mean position are $V_1$ and $V_2,$ respectively. Its time period is

hard

Oscillations

2015

physics

$2\pi \left[ \frac{x_2^2 - x_1^2}{{V_1^2 - V_2^2}} \right]^ \frac{1}{2}$

Explanation

To solve this problem, we need to use the properties of simple harmonic motion (SHM). $\\$ In SHM, the velocity $v$ of a particle at a distance $x$ from the mean position is given by: $\\ v = \omega \sqrt{A^2 - x^2} \\$

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A particle is executing SHM along a straight line. Its velocities at distances x1 x_1 x1​ and x2 x_2 x2​ from the mean position are V1 V_1 V1​ and V2, V_2, V2​, respectively. Its time period is

Explanation

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A particle is executing SHM along a straight line. Its velocities at distances $x_1$ and $x_2$ from the mean position are $V_1$ and $V_2,$ respectively. Its time period is