Question

When an object is in simple harmonic motion, and is moving in the vertical direction, the magnitude of its acceleration is at a minimum when it is:

a. At the highest point
b. At the lowest point
c. At either point
d. At the equilibrium point

Answer 1

The magnitude of acceleration is at a minimum when an object in simple harmonic motion is at the equilibrium point, where it passes through with maximum speed and where the restoring force is zero.

Step-by-step explanation:

When an object in simple harmonic motion (SHM) reaches the equilibrium position, it is moving at its maximum speed and has zero acceleration because it is at the midpoint of its motion. Therefore, the magnitude of acceleration of an object is at a minimum when it is at the equilibrium point. The equilibrium point is the position where the spring is neither stretched nor compressed, marked as x = 0. At the extremes of the motion, where the displacement is maximum (amplitude A), the velocity is zero and the acceleration is at its maximum, because the restoring force, which is proportional to the displacement, is strongest here.

In summary, for a vertical simple harmonic motion, commonly demonstrated by a mass attached to a spring, the acceleration is at a minimum at the equilibrium point, which is the position where the mass would naturally rest in the absence of a force. This is the point where the mass passes through with maximum speed as it oscillates with equal displacement on either side of the equilibrium.