Which of the following describes the motion of a mass attached to a horizontal spring undergoing simple harmonic motion?

• A. The mass oscillates back and forth around the equilibrium position with a restoring force proportional to its displacement, $F=-kx$.
• B. The mass moves in a circular path with a constant radius.
• C. The mass moves back and forth around the equilibrium position with a constant speed.
• D. The mass moves in a straight line with a constant acceleration.

Answer: (A)

Verified step by step guidance

1. Understand the concept of simple harmonic motion (SHM): In SHM, an object oscillates back and forth around an equilibrium position. The restoring force that brings the object back to the equilibrium position is proportional to the displacement from that position.
2. Identify the characteristics of SHM: The motion is periodic, meaning it repeats in a regular cycle. The speed of the object is not constant; it varies as the object moves through its cycle.
3. Analyze the options given: The first option describes the motion as oscillating back and forth with a restoring force proportional to displacement, which matches the definition of SHM.
4. Evaluate the incorrect options: The second option describes circular motion, which is not applicable to SHM. The third option suggests constant speed, which contradicts the varying speed in SHM. The fourth option implies constant acceleration, which is not characteristic of SHM.
5. Conclude that the correct description of the motion of a mass attached to a horizontal spring undergoing SHM is that it oscillates back and forth around the equilibrium position with a restoring force proportional to its displacement.