The displacement of a particle along the x-axis is given by x = asin2 ω t. The motion of the particle corresponds to (a) simple harmonic motion of frequency ω/π (b) simple harmonic motion of frequency 3ω/2π (c) non simple harmonic motion (d) simple harmonic motion of frequency ω/2π

Answer: (c). x = asin ²ω t = a/2 - a/2cos 2ω t. This is SHM of amplitude a/2 about the shifted mean position x = a/2, with angular frequency 2ω. Frequency f = (2ω)/(2π) = (ω)/(π). So the working gives (a) SHM of frequency ω/π; the key's (c) treats the shifted-mean motion as non-SHM.

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Periodic Motion & SHM Basics

The displacement of a particle along the x-axis is given by x = asin2 $\omega$ t. The motion of the particle corresponds to

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Answer: (c)

$x = a\sin^2\omega t = \frac{a}{2} - \frac{a}{2}\cos 2\omega t$ .
This is SHM of amplitude $a/2$ about the shifted mean position $x = a/2$ , with angular frequency $2\omega$ .
Frequency $f = \frac{2\omega}{2\pi} = \frac{\omega}{\pi}$ .
So the working gives (a) SHM of frequency $\omega/\pi$ ; the key's (c) treats the shifted-mean motion as non-SHM.

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