MHT CET 2024 16th May Evening Shift | Simple Harmonic Motion Question 3 | Physics

A particle performs linear S.H.M. At a particular instant, velocity of the particle is ' $u$ ' and acceleration is ' $\alpha$ ' while at another instant, velocity is ' $v$ ' and acceleration is ' $\beta$ ' $(0<\alpha<\beta)$. The distance between the two positions is

$\frac{u^2-v^2}{\alpha+\beta}$

$\frac{u^2+v^2}{\alpha+\beta}$

$\frac{u^2-v^2}{\alpha-\beta}$

$\frac{u^2+v^2}{\alpha-\beta}$

MHT CET 2024 16th May Morning Shift

MCQ (Single Correct Answer)

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A particle executing S.H.M. has velocities ' $\mathrm{V}_1$ ' and ' $\mathrm{V}_2$ ' at distances ' $x_1$ ' and ' $x_2$ ' respectively, from the mean position. Its frequency is

$\frac{1}{2 \pi} \sqrt{\frac{V_1^2-V_2^2}{x_1^2-x_2^2}}$

$2 \pi \sqrt{\frac{x_1^2-x_2^2}{v_1^2-V_2^2}}$

$\frac{1}{2 \pi} \sqrt{\frac{V_2^2-V_1^2}{x_1^2-x_2^2}}$

$2 \pi \sqrt{\frac{\mathrm{x}_1^2-\mathrm{x}_2^2}{\mathrm{~V}_2^2-\mathrm{V}_1^2}}$

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

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For a particle executing S.H.M. having amplitude A, the speed of the article is $\left(\frac{1}{3}\right)^{\text {rd }}$ of its maximum speed when the displacement from the mean position is

$\frac{3 \mathrm{~A}}{\sqrt{2}}$

$\frac{2 \mathrm{~A}}{3}$

$\frac{2 \sqrt{2}}{3} \mathrm{~A}$

$\frac{\sqrt{2}}{3} \mathrm{~A}$

MHT CET 2024 15th May Evening Shift

MCQ (Single Correct Answer)

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The motion of a particle is described by the equation $a=-b x$ where ' $a$ ' is the acceleration, x is the displacement from the equilibrium position and b is a constant. The periodic time will be

$\frac{2 \pi}{\mathrm{~b}}$

$\frac{2 \pi}{\sqrt{b}}$

$2 \pi \sqrt{b}$

$2 \sqrt{\frac{\pi}{b}}$

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