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(D) Given the position vector: $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$.Comparing this with $\overrightarrow{r} = x \wideha

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All of these

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(D) Given the position vector: $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$.Comparing this with $\overrightarrow{r} = x \widehat{i} + y \widehat{j}$,we get:$x = A \cos \omega t$  $...(1)$$y = 2A \cos \omega t$  $...(2)$From equation $(1)$,we have $\cos \omega t = \frac{x}{A}$. Substituting this into equation $(2)$:$y = 2A \left( \frac{x}{A} \right) = 2x$.Since $y = 2x$ represents a straight line passing through the origin,the motion is on a straight line.Since $x = A \cos \omega t$ and $y = 2A \cos \omega t$ are functions of time involving $\cos \omega t$,the particle oscillates about the origin,which is simple harmonic motion.Since the motion repeats itself after a time interval $T = \frac{2\pi}{\omega}$,the motion is periodic.Therefore,all the given statements are correct.

$A$ particle moves in the $x-y$ plane according to the equation $\overrightarrow{r} = (\widehat{i} + 2\widehat{j}) A \cos \omega t$. The motion of the particle is:

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