The correct option is **A. The displacement from equilibrium**. ### Detailed Explanation In simple harmonic motion (SHM), the key characteristic is that the restoring force acting on an object is directly proportional to its displacement from the equilibrium position. This relationship can be expressed mathematically using Hooke's Law, which states: \[ F = -kx \] Where: - \( F \) is the restoring force, - \( k \) is the spring constant (a measure of the stiffness of the spring), - \( x \) is the displacement from the equilibrium position. The negative sign indicates that the force acts in the opposite direction to the displacement, meaning that if the object is displaced to the right (positive \( x \)), the restoring force will act to the left (negative \( F \)), and vice versa. #### Why Option A is Correct: - **Proportionality**: The restoring force is proportional to the displacement \( x \). This means that as the displacement increases, the restoring force also increases linearly. This linear relationship is what characterizes simple harmonic motion. - **Equilibrium**: When the object is at the equilibrium position (where \( x = 0 \)), the restoring force is zero. As the object moves away from this position, the force increases, pulling it back towards equilibrium. ### Why the Other Options are Incorrect: **B. The velocity of the object** - The velocity of the object in SHM is not proportional to the restoring force. In fact, the velocity is highest as the object passes through the equilibrium position and is zero at the maximum displacement. The restoring force depends on displacement, not velocity. **C. The mass of the object** - While mass does play a role in the dynamics of motion (affecting acceleration and inertia), it is not directly proportional to the restoring force in SHM. The restoring force is independent of mass; it is determined solely by the displacement from equilibrium and the spring constant. **D. The acceleration due to gravity** - The acceleration due to gravity (\( g \)) is a constant that affects the weight of the object but does not influence the restoring force in SHM. The restoring force is related to the displacement and the properties of the spring or system in question, not the gravitational acceleration. ### Summary of Key Concepts: - **Restoring Force**: In SHM, the restoring force is proportional to the displacement from the equilibrium position. - **Hooke's Law**: This relationship is mathematically described by \( F = -kx \). - **Equilibrium**: At equilibrium, the restoring force is zero; it increases as the object moves away from this position. - **Independence from Other Factors**: The restoring force is not dependent on velocity, mass, or gravitational acceleration. ### Revision Summary: - The restoring force in SHM is proportional to the displacement from equilibrium (Option A). - Hooke's Law describes this relationship: \( F = -kx \). - Velocity and mass do not determine the restoring force in SHM. - Gravitational acceleration is unrelated to the restoring force in the context of SHM.