Question6: Explain why in SHM, the acceleration is zero when the velocity is greatest?

We know that if x₀ is the amplitude of simple harmonic motion and ‘x’ is the displacement of the oscillator from the mean position at any instant of time, then the instantaneous velocity of the oscillator is given by,

Similarly, it is the characteristic of SHM that the acceleration at any instant is proportional to its displacement from the mean position.

The negative sign accounts for the fact that the acceleration is directed to the center.

Now in equation (A), velocity of the oscillator will be maximum if x = 0, i-e, when the oscillator is at the central point. So,

Now in order to see what happens to the acceleration when the velocity is maximum, put x = 0 in equation (B).

Therefore x = 0 gives maximum velocity.It also gives a = 0. Therefore, when velocity is maximum, acceleration is zero.

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Follow up question.
(1) Why is acceleration zero at mean position?
(2) Where is the acceleration greatest in SHM?