The correct answer is: B. Proportional to A2
The total energy of a particle executing simple harmonic motion is given by the equation:
$$E = \frac{1}{2}m\omega^2A^2$$
where $m$ is the mass of the particle, $\omega$ is the angular frequency of the motion, and $A$ is the amplitude of the motion.
The angular frequency of the motion is given by the equation:
$$\omega = \frac{2\pi}{T}$$
where $T$ is the period of the motion.
The period of the motion is given by the equation:
$$T = \frac{2\pi}{\sqrt{k/m}}$$
where $k$ is the spring constant.
Therefore, the total energy of the particle is given by the equation:
$$E = \frac{1}{2}m\left(\frac{2\pi}{\sqrt{k/m}}\right)^2A^2 = \frac{4\pi^2}{m}k A^2$$
Since $k$ is a constant, the total energy of the particle is proportional to the square of the amplitude of the motion.