Amass on a spring undergoes shm. when a mass passes through the equilibrium position, which of the following statements about it are true

a) Its kinetic energy is a maximum.

b) Its acceleration is zero.

c) Its elastic potential energy is zero.                

Explanation:

A mass spring system will trace a sinusoidal curve as a function of time, similar to any object vibrating in simple harmonic motion.

a. In a two and fro motion, the velocity of the mass is greatest at the center, thus the kinetic energy is maximum at the equilibrium position.

b. At the equilibrium position, the total energy of the system is in the form kinetic energy and the potential energy is zero. Therefore there no force exerted on the mass. Since there is no force and the velocity of the mass is maximum , acceleration of the mass is zero.

c. The total energy in the mass spring system is comprised of potential energy and kinetic energy. Since the energy is conserved in nature, the kinetic energy at the equilibrium position is maximum and therefore the potential energy should be zero at the equilibrium position.

Explanation:

When a particle under goes simple harmonic motion, it oscillates between the two extreme positions in which a means position or the equilibrium position lies.

At equilibrium position, the potential energy of the body is zero but the kinetic energy is maximum and hence the velocity of the body is also maximum at the extreme position.

At extreme position, the kinetic energy is zero but the potential energy is maximum. The velocity is also zero at its extreme position.