Question

When are the displacement and acceleration equal to zero for the motion of a mass on a spring?

A) At maximum displacement

B) At minimum displacement

C) At the equilibrium position

D) At a displacement of -X

Answer 1

For a mass on a spring in simple harmonic motion, both displacement and acceleration are zero at the equilibrium position, which is when the spring is neither stretched nor compressed.

Step-by-step explanation:

This pertains to simple harmonic motion (SHM) and specifically asks when the displacement and acceleration are both equal to zero for a mass on a spring. In SHM, the equilibrium position is where the object would naturally rest if not disturbed, that is, where the spring is neither stretched nor compressed. At this position, marked as x = 0, the net force on the mass is zero, and therefore the acceleration is zero. Since the object is at rest at this position, the displacement is also zero relative to the equilibrium position. Therefore, the correct answer to the student's question is C) At the equilibrium position.