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The displacement of a particle along the x-axis is given by x = a sin² ?t

The displacement of a particle along the x-axis is given by x = a sin² ?t. The motion of the particle corresponds is:

Options

(a) simple harmonic motion of frquency ? / π
(b) simple harmonic motion of frequency 3? / 2π
(c) non simple harmonic motion
(d) simple harmonic motion of frquency ? / 2π

Correct Answer:

simple harmonic motion of frquency ? / π

Explanation:

x = a sin² ?t = a/2 (1 – cos 2 ?t)
dx/ dt = 2? sin 2 ?t
⇒ d²x/ dt² = 4?ￂﾲa / 2 . cos 2 ?t
This represents an S.H.M. of frequency
? / π

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