Question

A particle moves in x-y plane according to equation $\overrightarrow{S}=(2\hat{i}+\hat{j})cos\omega t$ The motion of particle is

• A. On straight line
• B. On ellipse
• C. Periodic
• D. SHM

Answer 1

Answer: (A), (C), (D)

The correct options are
A On straight line
C Periodic
D SHM

$S=(2\hat{i}+\hat{j})cos\omega t=(2cos\omega t\hat{i}+cos\omega t\hat{j})x=2cos\omega t$ . . . . (i)
$y=cos\omega t$ . . . . (ii)
Both represent SHM's equations and phase difference $\varphi$ = 0
Also $A_1\ne A_2$
so resulting motion of particle is S.H.M with
$A=\sqrt{A_1^2+A_2^2}=\sqrt{4+1}=\sqrt{5}$
Slope = $tan\theta =\frac{1}{2}$, hence path is a straight line
So motion is S.H.M and periodic