The correct answer is: A. Zero potential energy and maximum kinetic energy.
When a particle is at its maximum displacement, it has the maximum distance from its equilibrium position. This means that its potential energy is at a minimum, since potential energy is inversely proportional to distance from the equilibrium position. At the same time, its kinetic energy is at a maximum, since kinetic energy is proportional to the square of the particle’s velocity. This is because the particle has to travel the fastest in order to reach its maximum displacement.
Option B is incorrect because the particle has some kinetic energy at its maximum displacement. Option C is incorrect because the particle has no potential energy at its maximum displacement. Option D is incorrect because the particle has some kinetic energy at its maximum displacement.