How long after the beginning of motion is the displacement of a harmonically oscillating particle equal to one half its amplitude if the period is 24s and particle starts from rest.

12s

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Solution

The correct option is C 4s
equation of SHM is
$y = A c o s (ω t)$
As it is given displacement is half the amplitude
$y = \frac{A}{2}$
$\frac{A}{2} = A c o s (ω t)$
$c o s (ω t) = \frac{1}{2}$
$ω t = \frac{π}{3}$
$\frac{2 π}{24} t = \frac{π}{3}$
$t = 4 s$

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How long after the beginning of motion is the displacement of a harmonically oscillating particle equal to one half its amplitude if the period is 24s and particle starts from rest.

The correct option is C 4sequation of SHM isy=Acos(ωt)As it is given displacement is half the amplitudey=A2A2=Acos(ωt)cos(ωt)=12ωt=π32π24t=π3t=4s

The correct option is C 4s
equation of SHM is
$y = A c o s (ω t)$
As it is given displacement is half the amplitude
$y = \frac{A}{2}$
$\frac{A}{2} = A c o s (ω t)$
$c o s (ω t) = \frac{1}{2}$
$ω t = \frac{π}{3}$
$\frac{2 π}{24} t = \frac{π}{3}$
$t = 4 s$