First slide

Simple hormonic motion

Question

A particle is moving along x-axis and its position is given by $x = 2 \cos^{2} 4 πt cm$ . Then

Moderate

A

The particle does not execute simple harmonic motion
B

The particle executes simple harmonic motion about the point x = 1 cm
C

amplitude of oscillation of the particle is 1 cm
D

both (2) and (3) are right

Solution

$x = 2 \cos^{2} 4 πt = (1 + \cos 8 πt)$
From this equation it is evident that equilibrium position of the particle is at x = 1 cm (point A). Amplitude of oscillation is 1cm. Origin O and point B are extreme positions of the particle.

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