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  4. Velocity at mean position of a particle executing S.H.M. is v, then velocity of the t particle at a distance equal to half of the amplitude;

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Q. Velocity at mean position of a particle executing S.H.M. is $v$, then velocity of the t particle at a distance equal to half of the amplitude;

Rajasthan PMTRajasthan PMT 2001Oscillations

Solution:

Velocity in mean position $v=a \omega$, velocity at a distance of half amplitude.
$v'=\omega \sqrt{a^{2}-y^{2}}$
$=\omega \sqrt{a^{2}-\frac{a^{2}}{4}}$
$=\sqrt{\frac{3}{2}} a \omega=\sqrt{\frac{3}{2} v}$