The two-dimensional motion of a particle, described by $\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$ is…
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:
B, C and D only
A, B and C only
A, C and D only
C and D only
Solution
$\vec{r}=(\hat{i}+2 \hat{j}) A \cos \omega t$
$x=A \cos \omega t$
$y=2 A \cos \omega t$
$y=2 x$
The path is straight line.
The motion is SHM and periodic as
$\frac{d r}{d t}=-(\hat{i}+2 \hat{j}) \omega A \sin \omega t$
$\frac{d^2 r}{d t^2}=-(\hat{i}+2 \hat{j}) \omega^2 A \cos \omega t$
$\vec{a}=-\omega^2 \vec{r}$