The two-dimensional motion of a particle, described by r = (i+2j)Acos… | NEET 2024

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Damped, Forced Oscillations & Superposition

The two-dimensional motion of a particle, described by $\vec{r} = (\hat{i}+2\hat{j})A\cos\omega t$ is a/an: A. parabolic path

B. elliptical path

C. periodic motion

D. simple harmonic motion

Choose the correct answer from the options given below:

Show answer and solution

Answer: (d)

$x = A\cos\omega t$ , $y = 2A\cos\omega t \Rightarrow y = 2x$ : a straight line, not a parabola or ellipse.
Position repeats every $2\pi/\omega$ , so the motion is periodic.
$\vec{r} \propto \cos\omega t$ along a fixed line, so $\vec{a} = -\omega^2\vec{r}$ : SHM.
So the answer is (d) C and D only.

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