The periodic time of $SHM$ is also measured by $T = 2 \pi \sqrt{\frac{\text{displacement}}{\text{acceleration}}}$. Can we say that the time period depends on the displacement?

(N/A) No,the time period does not depend on the displacement. In $SHM$,the acceleration $a$ is directly proportional to the displacement $x$,given by the relation $a = -\omega^2 x$. When we substitute this into the formula,the displacement terms cancel out: $T = 2 \pi \sqrt{\frac{x}{\omega^2 x}} = 2 \pi \sqrt{\frac{1}{\omega^2}} = \frac{2 \pi}{\omega}$. Thus,the time period is independent of the displacement.