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(B) The given equation of motion is $x = a \cos(\alpha t)$.This represents a Simple Harmonic Motion $(SHM)$ where the particle oscillates about the me

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Periodic and oscillatory

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(B) The given equation of motion is $x = a \cos(\alpha t)$.This represents a Simple Harmonic Motion $(SHM)$ where the particle oscillates about the mean position $x = 0$ between the limits $x = +a$ and $x = -a$.$1$. $A$ motion is called periodic if it repeats itself at regular intervals of time. Here,the time period is $T = \frac{2\pi}{\alpha}$,so the motion is periodic.$2$. $A$ motion is called oscillatory if the particle moves to and fro about a fixed mean position. Since the particle oscillates between $x = +a$ and $x = -a$ about the mean position $x = 0$,the motion is oscillatory.Therefore,the motion is both periodic and oscillatory.

The equation of motion of a particle is $x = a \cos(\alpha t)$. The motion is

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