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A particle executes S.H.M. The acceleration of the particle is maximum

  • A.at extreme position
  • B.at mean position
  • C.midway between mean and extreme position
  • D.acceleration is same at all position

Answer: A

The acceleration is maximum at the extreme position.

In simple harmonic motion the acceleration is proportional to the displacement from the mean position and directed towards it:

\[ a = -\omega^{2} x \]

The displacement is largest, equal to the amplitude, at either extreme, so the acceleration is largest there too. At the mean position x = 0, so the acceleration is zero, while the speed is at its maximum.

So 'at mean position' confuses acceleration with velocity, the midway point gives only half the maximum value, and the acceleration is clearly not the same everywhere because it changes with x.

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