A small mass executes linear $SHM$ about $O$ with amplitude $a$ and period $T.$ Its displacement from $O$ at time $T/8$ after passing through $O$ is :
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This SHM can be represented by
$\boldsymbol{x}=\boldsymbol{a} \sin \omega t$
$\Rightarrow x=a \sin \frac{2 \pi t}{T}$
$\Rightarrow x\left(t=\frac{T}{8}\right)=a \sin \left(\frac{2 \pi}{T} \times \frac{T}{8}\right)=a \sin \left(\frac{\pi}{4}\right)=\frac{a}{\sqrt{2}}$
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