AIIMS 2018 Physics Simple Harmonic Motion MCQ Question

In simple harmonic motion (SHM), the displacement $x$ from the mean position can be described by the equation $x = A \cos(\omega t)$, where $\omega = \frac{2\pi}{T}$. To find the time taken to travel a distance of $\frac{A}{5}$ starting from rest, we set up the equation $A - \frac{A}{5} = A \cos(\omega t)$, leading to $\cos(\omega t) = \frac{4}{5}$. Solving for $t$ gives $t = \frac{T}{2\pi} \cos^{-1}\left(\frac{4}{5}\right)$, confirming option B as correct.

Options A, C, and D are incorrect because they do not yield the correct relationship between time and the cosine function derived from the displacement equation; specifically, they either miscalculate the angle or do not account for the correct amplitude change in the context of SHM.