Q 11-13-146JEE MainJEE Main 2018 (15 Apr, Shift 2)Medium
Two simple harmonic motions, $x(t) = A\sin(at + \delta)$ and $y(t) = B\sin(bt)$, are at right angles. They are combined to form Lissajous figures. Identify the correct match below.
Answer: (C) Parameters: $A \ne B,\ a = b,\ \delta = \dfrac\pi2$; Curve: Ellipse
With $a = b$ and $\delta = \dfrac\pi2$: $x = A\cos(bt)$ and $y = B\sin(bt)$, so
$$\frac{x^2}{A^2} + \frac{y^2}{B^2} = 1$$
an ellipse when $A \ne B$ (a circle when $A = B$). Option (3) is correct.
The others fail: $A = B$, $a = b$, $\delta = \frac\pi2$ gives a circle, not a line; $a = b$, $\delta = 0$ gives the straight line $y = \frac BA x$, not a parabola; $a = 2b$ with $\delta = \frac\pi2$ gives a figure-of-eight type curve, not a circle.
Solution by Sreeraj P, M.Sc Physics