Final answer:
At the point of maximum displacement in a mass-spring system undergoing simple harmonic motion, the velocity of the mass is zero, and the potential energy of the system is at its maximum, while kinetic energy is zero.
Step-by-step explanation:
At the point where a mass m attached to a spring with spring constant k achieves its maximum displacement from the equilibrium position in simple harmonic motion (SHM), several specific conditions are met. At this point, which corresponds to the amplitude of the motion, the velocity of the mass is zero. This occurs because motion has directionally reversed from moving towards the extreme position to moving back towards equilibrium.
Therefore, the statement that the velocity is zero at maximum displacement is true. Since there is no velocity at this point, it means all the energy of the system is stored as potential energy (U = ½kA²) in the spring, leading to the conclusion that the potential energy is at its maximum. On the other hand, the kinetic energy (KE = ½mv²) is zero because the velocity (v) is zero. Finally, the acceleration is not zero; it is at its maximum because the restoring force, which is directly proportional to the displacement, is maximal at this point and is what accelerates the mass back toward the equilibrium position.
The correct answer to the question is that at the point of maximum displacement in a mass-spring system undergoing SHM, (a) The velocity is zero and (c) The potential energy is at its maximum.