### Correct Option: B. The displacement from the equilibrium position ### Detailed Explanation: In simple harmonic motion (SHM), the key characteristic is that the acceleration of the oscillating object is directly proportional to its displacement from the equilibrium position. This relationship can be expressed mathematically using Hooke's Law and the equations of motion. 1. **Understanding Simple Harmonic Motion**: - SHM occurs when an object oscillates back and forth around a central equilibrium position. The motion is periodic, meaning it repeats itself at regular intervals. - The equilibrium position is the point where the net force acting on the object is zero. 2. **Acceleration in SHM**: - The acceleration \( a \) of an object in SHM can be described by the formula: \[ a = -\omega^2 x \] where: - \( a \) is the acceleration, - \( \omega \) is the angular frequency (related to the frequency of the motion), - \( x \) is the displacement from the equilibrium position. - The negative sign indicates that the acceleration is directed towards the equilibrium position, meaning it acts in the opposite direction to the displacement. 3. **Proportionality**: - From the equation \( a = -\omega^2 x \), we can see that the acceleration \( a \) is directly proportional to the displacement \( x \). This means that as the displacement increases, the acceleration also increases (in magnitude), and vice versa. ### Why Other Options Are Incorrect: - **A. The mass of the object**: - The mass of the object does not affect the acceleration in SHM directly. While mass is a factor in determining the force (via \( F = ma \)), the acceleration itself is not proportional to mass. Instead, it is determined by the restoring force and the displacement. - **C. The velocity of the object**: - The velocity in SHM is not directly proportional to the acceleration. In fact, at maximum displacement, the velocity is zero, and at the equilibrium position, the velocity is at its maximum. Therefore, there is no direct proportionality between acceleration and velocity in SHM. - **D. The frequency of the motion**: - While frequency does relate to the motion (as it determines how fast the oscillations occur), it is not directly proportional to the acceleration. The frequency is related to the angular frequency \( \omega \) (where \( \omega = 2\pi f \)), but the acceleration itself depends on the displacement, not the frequency. ### Summary of Key Points: - In simple harmonic motion, acceleration is directly proportional to the displacement from the equilibrium position. - The relationship is given by the formula \( a = -\omega^2 x \). - Mass, velocity, and frequency do not directly determine the acceleration in SHM. - Understanding the relationship between displacement and acceleration is crucial for solving problems related to SHM. This thorough understanding of SHM will help you tackle related questions effectively in your exams!