Which graph represents the difference between total energy and potential energy of a particle executing SHM vs its distance from mean position?

Given: Which graph represents (Total Energy - Potential Energy) vs distance from mean position for SHM?

Identify the quantity.

Total Energy $$E = \frac{1}{2}kA^2$$ (constant)

Potential Energy $$U = \frac{1}{2}kx^2$$

$$E - U = \frac{1}{2}kA^2 - \frac{1}{2}kx^2 = \frac{1}{2}k(A^2 - x^2)$$

This is the kinetic energy, which is a downward-opening parabola with maximum at $$x = 0$$ and zero at $$x = \pm A$$.

Graph description.

The graph is an inverted parabola (concave down) with maximum value $$\frac{1}{2}kA^2$$ at the mean position and zero at the extremes $$\pm A$$.

The correct answer is Option C: a downward parabola (concave down).