Question

A particle moves in x-y plane according to the equation $\overrightarrow{r}=(\hat{i}+\hat{j})$ ( A sin $\omega$t + B cos $\omega$t ). Motion of the particle is:

• A. periodic
• B. SHM
• C. along a straight line
• D. along an ellipse

Answer 1

The correct option is D along an ellipse

$\begin{array}{c}{x}^2=a^2{\sin }^2\omega t..............\left(1\right)\\ y^2=a^2{\cos }^2\omega t..............\left(2\right)\\ fromeq\left(1\right)+eq\left(2\right)\\ x^2+y^2=a^2\\ Whichisacirclesequation.\\ Thereforeitfollowsacircularpath.\end{array}$

Motion of the particle is along an ellipse.

Hence,

Option $D$ is correct answer.