QJEEM18Phc50b: JEE Main 2018 Physics - Class 11 JEEM18Phc50b Solution: Two simple harmonic motions, as shown below, are at right…

The given simple harmonic motions to form Lissajous figures are $x(t) = A\sin (at + \delta )$ and $y(t) = B\sin (bt)$ .

For parabola, conditions should be

A = B or A $\ne$ B, a = 2b, $\delta$ = $\pi$ /2

For line, conditions should be

A = B, a = b, $\delta$ = $\pi$

For circle, condition should be

A = B, a = b; $\delta$ = $\pi$ /2

For ellipse, condition should be

A $\ne$ B, a = b; $\delta$ = $\pi$ /2

Therefore, we obtain an ellipse.