A body is executing simple harmonic motion if:

Explanation

In simple harmonic motion (SHM), a body moves in such a way that its acceleration is directly proportional to its displacement from a fixed point (the mean position) and is always directed towards that point. This results in an oscillatory motion characteristic of SHM, such as in a spring-mass system or a pendulum. Therefore, Option A is correct because it accurately describes this relationship and directionality.Option B is incorrect because the acceleration is not inversely proportional, nor is it directed away from the mean position. Option C is incorrect because, although it mentions the correct direction towards the mean position, it incorrectly describes the relationship as inversely proportional. Option D is incorrect because although it correctly states the direct proportionality, it wrongly claims the direction is away from the mean position.