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The displacement of aparticle along the x-axis is given by $x = a$ $\sin^{2} ω t$ .
The motion of the particle corresponds to:

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non simple harmonic motion

simple harmonic motion of frequency $\frac{ω}{π}$

simple harmonic motion of frequency $\frac{ω}{2 π}$

simple harmonic motion of frequency $\frac{3 ω}{2 π}$

answer is A.

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Detailed Solution

$x = a \sin^{2} ω t = \frac{a}{2} (1 - \cos 2 ω t)$

$\begin{array}{l} \frac{dx}{dt} = \frac{a}{2} 2 ω \sin 2 ω t \\ = \frac{d^{2} x}{{dt}^{2}} = \frac{4 ω^{2} a}{2} \cdot \cos 2 ω t \end{array}$

This represents an S. H. M. of frequency $= \frac{ω}{π}$

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