The correct answer is: B. proportional to A2
The total energy of a particle executing simple harmonic motion is given by the equation $E = \frac{1}{2}kA^2$, where $k$ is the spring constant. The spring constant is a measure of the stiffness of the spring, and it is proportional to the force required to stretch or compress the spring by a unit distance. The amplitude of the motion is the maximum displacement of the particle from its equilibrium position.
The total energy of a particle executing simple harmonic motion is proportional to the square of the amplitude. This is because the potential energy of the particle is proportional to the square of the displacement, and the kinetic energy of the particle is proportional to the square of the velocity. The velocity of the particle is maximum when it is at its equilibrium position, and the displacement is zero at this point. Therefore, the potential energy of the particle is maximum at this point, and the kinetic energy of the particle is zero. As the particle moves away from its equilibrium position, its potential energy decreases and its kinetic energy increases. When the particle reaches its maximum displacement, its potential energy is zero and its kinetic energy is maximum. As the particle moves back towards its equilibrium position, its kinetic energy decreases and its potential energy increases. When the particle reaches its equilibrium position, its kinetic energy is zero and its potential energy is maximum.
The total energy of the particle is the sum of its potential energy and its kinetic energy. Therefore, the total energy of the particle is proportional to the square of the amplitude.