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  4. A particle undergoes simple harmonic motion having time period T. The time taken in 3 / 8 th oscillation is

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Q. A particle undergoes simple harmonic motion having time period $T$. The time taken in $3 / 8$ th oscillation is

Solution:

$y=\frac{a}{2}=a \cos \omega t=a \cos \frac{2 \pi}{T} t$ or $t=\frac{T}{6} s$
So time complete $3 / 8^{\text {th }}$ oscillation
$=\frac{T}{4}+\frac{T}{6}=\frac{5 T}{6}$