Question

The structural characteristics of Simple Harmonic Motion (SHM) require that the acceleration of a particle is directly proportional to its displacement from the mean position and is directed:

• A. along the direction of motion
• B. opposite to the direction of velocity at all times
• C. towards the mean position
• D. away from the mean position

Hint:

In SHM: \[ a = -\omega^2 x \Rightarrow restoring nature always \]

Answer 1

The Correct Option is C

Step 1: Understand simple harmonic motion.
In this motion a particle moves back and forth about a fixed central point called the mean position. We want to know which way its acceleration points.

Step 2: Recall the defining rule.
The key feature is that the acceleration is proportional to the displacement but pulls the particle back. We write \[ a = -\omega^2 x. \]

Step 3: Read the minus sign.
The minus sign is the heart of the answer. It means the acceleration is opposite in direction to the displacement from the centre.

Step 4: See what opposite means.
If the particle is to the right of the centre, the acceleration points left, back toward the centre. If it is to the left, the acceleration points right, again toward the centre.

Step 5: Rule out the other choices.
It is not along the motion, since the particle can move away while being pulled back. It is not always opposite the velocity. And pointing away would make the motion fly apart, which does not happen.

Step 6: State the answer.
The acceleration always points back to the centre, that is, toward the mean position. \[ \boxed{\text{towards the mean position}} \]