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  4. A particle executes a simple harmonic motion of time period T . Find the time taken by the particle to go directly from its mean position to half the amplitude

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Q. A particle executes a simple harmonic motion of time period $ T $ . Find the time taken by the particle to go directly from its mean position to half the amplitude

MHT CETMHT CET 2011

Solution:

$y=a \sin \omega t=\frac{a \sin 2 \pi}{T} t$
At the mean position $y=\frac{a}{2}$
$\frac{a}{2}=\frac{a \sin 2 \pi t}{T}$
$t=\frac{T}{12}$