Question 241: Oscillations

Question

A particle executes S.H.M. starting from the mean position. Its amplitude is ' a ' and its periodic time is ' $T$ '. At a certain instant, its speed ' $u$ ' is half that of maximum speed $\mathrm{V}_{	ext {max }}$. The displacement of the particle at that instant is

Accepted Answer

Speed at displacement x
$$ u=\omega \sqrt{a^2-x^2} $$
Speed of particle at a certain instant is half that of maximum speed $\mathrm{V}_{	ext {max }}$
$$ \begin{array}{ll} 	herefore & \mathrm{u}=\frac{\mathrm{V}_{\max }}{2}=\frac{\omega \mathrm{a}}{2} \ 	herefore & \frac{\omega \mathrm{a}}{2}=\omega \sqrt{\mathrm{a}^2-\mathrm{x}^2} \ & \mathrm{a}^2-\mathrm{x}^2=\frac{\mathrm{a}^2}{4} \ & \mathrm{x}^2=\frac{3}{4} \mathrm{a}^2 \ & \mathrm{x}=\frac{\sqrt{3}}{2} \mathrm{a} \end{array} $$

Answer

$\frac{2 \mathrm{a}}{\sqrt{3}}$

Answer

$\frac{\sqrt{2} \mathrm{a}}{3}$

Answer

$\frac{3 \mathrm{a}}{\sqrt{2}}$

Answer

$\frac{\sqrt{3} \mathrm{a}}{2}$

Oscillations

A particle executes S.H.M. starting from the mean position. Its amplitude is ' a ' and its periodic time is ' T '. At a certain instant, its speed ' u ' is half that of maximum speed \mathrm{V}_{\text {max }}. The displacement of the particle at that instant is

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