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x = a sin²ωt = a/2 (1 - cos 2ωt). This represents an S.H.M. of frequency ω/π.

1. x = a sin²ωt = a/2 (1 - cos 2ωt)
2. dx/dt = a/2 ω sin 2ωt
3. d²x/dt² = 4ω²a/2 cos 2ωt
4. This represents an S.H.M. of frequency ω/π.

Correct answer: This represents an S.H.M. of frequency ω/π.

Solution

The given equation x = a sin²ωt = a/2 (1 - cos 2ωt) represents a motion that is not simple harmonic motion (S.H.M.) because it involves a squared sine term, which leads to a frequency of 2ω, not ω/π. Thus, option D is correct as it correctly identifies the statement about frequency.

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