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;

Question

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; (A)  4v (B)  2v (C)  (√3/2)v (D)  (√3/4)v

Tardigrade Admin · Accepted Answer

Velocity in mean position v=a ω, velocity at a distance of half amplitude. v'=ω √a2-y2 =ω √a2-(a2/4) =√(3/2) a ω=√(3/2) v

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;

$4 v$

$2 v$

$\frac{3}{2} v$

$\frac{3}{4} v$

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

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;

4v

2v

23​​v

43​​v