The position vector of a particle is given by $\vec{r}=(3\hat{i}-4\hat{j}) A \sin \omega t$. This mo

Question

The position vector of a particle is given by $\vec{r}=(3\hat{i}-4\hat{j}) A \sin \omega t$. This motion is a/an A. straight line path B. elliptical path C. periodic path D. simple harmonic motion. Choose the correct answer from the options given below:

Professor PC Thomas Classes · Answer

(b) : Given $\vec{r}=(3\hat{i}-4\hat{j})A\sin\omega t$. \ Let $x = 3A\sin\omega t$ and $y = -4A\sin\omega t$. \ Dividing the two gives $y = -\frac{4}{3}x$, which is the equation of a straight line passing through the origin. \ Since the position depends on a sine function, the particle oscillates to and fro along this straight line. Thus, the motion is simple harmonic (SHM) and periodic. Hence A, C, and D are correct.