RE-NEET 2026 Physics Simple Harmonic Motion MCQ Question

In a simple harmonic oscillator, the relationship between position $x$ and velocity $v$ can be derived from the conservation of energy. The total mechanical energy is given by:

$E = \frac{1}{2} k x^2 + \frac{1}{2} m v^2$

For the graph of $v$ versus $x$ to be a circle, the equation must represent a constant total energy, which leads to the condition:

$\frac{v^2}{\frac{k}{m}} + \frac{x^2}{\frac{2E}{k}} = 1$

This implies that $\frac{k}{m} = 1$, or $k = m$.

The other options fail because they do not satisfy the circular relationship required for the graph in the $x-v$ plane.