The two dimensional motion of a particle, described by $\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$

Question

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 path D. simple harmonic motion Choose the correct answer from the options given below:

Professor PC Thomas Classes · Answer

(d) : $\vec{r}=A \cos \omega t \hat{i}+2 A \cos \omega t \hat{j}$ $$ \begin{aligned} & x=A \cos \omega t \ & y=2 A \cos \omega t \end{aligned} $$ Dividing (i) by (ii), we get $\frac{x}{y}=\frac{1}{2}$ [Equation of straight line]