In the following table,time is in column-$I$ and the phase of an oscillator starting from the mean position is in column-$II$. Match them appropriately.
Column-$I$ Column-$II$
$(a)$ $t = \frac{T}{8}$ $(i)$ $\theta = \frac{5\pi}{4}$
$(b)$ $t = \frac{5T}{8}$ $(ii)$ $\theta = \frac{3\pi}{2}$
$(iii)$ $\theta = \frac{\pi}{4}$

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(A) For an oscillator starting from the mean position,the displacement is given by $x = A \sin(\omega t)$.
The phase $\theta$ is given by $\theta = \omega t = \left(\frac{2\pi}{T}\right)t$.
For $(a)$ $t = \frac{T}{8}$,the phase is $\theta = \left(\frac{2\pi}{T}\right) \times \left(\frac{T}{8}\right) = \frac{\pi}{4}$. Thus,$(a-iii)$.
For $(b)$ $t = \frac{5T}{8}$,the phase is $\theta = \left(\frac{2\pi}{T}\right) \times \left(\frac{5T}{8}\right) = \frac{5\pi}{4}$. Thus,$(b-i)$.
Therefore,the correct matching is $(a-iii, b-i)$.

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