Which one of the following four particlcs, whose displacement .t and acceleration ax are related as follows, is executing simple harmonic motion ?

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Q: 56 (NDA-II/2016)

Which one of the following four particlcs, whose displacement .t and acceleration ax are related as follows, is executing simple harmonic motion ?

question_subject: 

Science

question_exam: 

NDA-II

stats: 

0,1,12,3,9,0,1

keywords: 

{'simple harmonic motion': [0, 0, 4, 4], 'acceleration ax': [0, 0, 0, 1], 'particlcs': [0, 0, 0, 1], 'ix': [0, 0, 1, 2]}

In simple harmonic motion (SHM), the acceleration of a particle is directly proportional to its displacement but in the opposite direction. Looking at the options provided:

Option 1: ax = +3x

This equation does not follow the criteria of SHM because the acceleration and displacement are in the same direction.

Option 2: az = +3t^2

This equation is not related to displacement and does not follow the criteria of SHM.

Option 3: No equation provided.

This option does not provide any information to determine if the particle is executing SHM or not.

Option 4: ax = -x

This equation follows the criteria of SHM. The acceleration is directly proportional to the displacement, and they are in opposite directions. Therefore, option 4 is the correct answer.

Overall, option 4 is the only option that satisfies the requirements for executing simple harmonic motion.