In a simple harmonic motion, acceleration of a particle is proportional toSelect one:a. Rate of change of velocityb. Velocityc. Displacementd. Direction

Break Down the Problem

1. Identify the options provided.
2. Understand the key characteristics of simple harmonic motion (SHM).

Relevant Concepts

Simple harmonic motion is characterized by the fact that the acceleration of the particle is directly proportional to its displacement from the equilibrium position and is directed towards that position. This can be represented mathematically as: $a = -k x$ where $a$ is the acceleration, $k$ is a constant, and $x$ is the displacement from the equilibrium position.

Analysis and Detail

1. Rate of change of velocity - This relates to acceleration but is not the defining characteristic of SHM.
2. Velocity - While velocity is a factor in SHM, the defining relationship is not based on velocity.
3. Displacement - This directly corresponds to the defining equation of SHM, indicating that acceleration is proportional to displacement.
4. Direction - While direction is important, it does not describe the proportionality that defines SHM.

Verify and Summarize

The acceleration in SHM is indeed proportional to the displacement from the equilibrium position. Thus, the correct answer, based on the characteristics of SHM, is:

Final Answer

c. Displacement