STANDARD Physics Simple Harmonic Motion MCQ Question

In simple harmonic motion (SHM), the mean velocity over a quarter oscillation can be calculated by considering the displacement covered in that time. For a particle with amplitude $A$ and time period $T$, the distance traveled in a quarter period (from $x = 0$ to $x = A$) is $A$, and the time taken is $T/4$. Thus, the mean velocity is given by $\text{Mean Velocity} = \frac{\text{Distance}}{\text{Time}} = \frac{A}{T/4} = \frac{4A}{T}$, which simplifies to $2A/T$ when considering the average over the full oscillation.

Options (A), (C), and (D) do not correctly account for the distance and time relationship in the context of quarter oscillation, leading to incorrect values for mean velocity.