Question

A particle moves in the X-Y plane according to the equation
$\overrightarrow{r}=\left(\overrightarrow{i}+2\overrightarrow{j}\right)A\cos \omega t.$
The motion of the particle is
(a) on a straight line
(b) on an ellipse
(c) periodic
(d) simple harmonic

Answer 1

(a) on a straight line
(c) periodic
(d) simple harmonic

The given equation is a solution to the equation of simple harmonic motion. The amplitude is $(\stackrel{\rightharpoonup }{i}+2\stackrel{\rightharpoonup }{j})A$, following equation of straight line y = mx + c. Also, a simple harmonic motion is periodic.