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  4. A particle executing SHM covers a distance equal to half its amplitude in 1 second. The time period of the particle is

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Q. A particle executing $SHM$ covers a distance equal to half its amplitude in $1$ second. The time period of the particle is

Oscillations

Solution:

In $SHM , x=A \sin \omega t=A \sin \frac{2 \pi}{T} t$
At $t=1 s , x=\frac{A}{2} $
$\therefore \,\,\,\,\,\frac{A}{2}=A \sin \frac{2 \pi}{T}$ or $\frac{1}{2}=\sin \frac{2 \pi}{T}$
or $\sin \frac{\pi}{6}=\sin \frac{2 \pi}{T}$ or $T=12 s$