The equation of motion of a particle is `x=acos(alphat)^(2)`. The motion is

Options

A. eriodic but not oscillatory
B. periodic and oscillatory
C. oscillatory but not periodic
D. neither periodic nor oscillatory

Explanation

To determine the nature of the motion described by the equation \( x = a \cos(\alpha t^2) \), we can analyze the equation step by step.

### Step 1: Identify the form of the equation
The equation given is \( x = a \cos(\alpha t^2) \). This indicates that the position \( x \) of the particle is a function of time \( t \) through the cosine function, which is characteristic of oscillatory motion.

### Step 2: Analyze the argument of the cosine function
In the equation, the argument of the cosine function is \( \alpha t^2 \). Unlike simple harmonic motion, where the argument is linear in time (like \( \omega t \)), here we have a quadratic dependence on time (i.e., \( t^2 \)). This suggests that the motion is not simple harmonic.

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