Q. Which of the following combination of Lissajous’ figure will be like eight (8)?
A) $x = a\sin{4\omega t,\ y = b\sin{\omega t}}$
B) $x = a\sin{2\omega t,\ y = b\sin{\omega t}}$
C) $x = a\sin{2\omega t,\ y = b\sin{2\omega t}}$
D) $x = a\sin{\omega t,\ y = b\sin{4\omega t}}$
Explanation
(b) If two SHMs act in perpendicular directions, then their resultant motion is in the form of a straight line or a circle or a parabola etc, depending on the frequency ratio of two SHMs and initial phase difference.
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For the frequency ratio $\omega_{1}:\omega_{2} = 2:1$, the two perpendicular SHMs are
$x = a\sin\left( \omega_{1} + \varnothing \right)\ and\ \ \ y = b\sin{\omega_{2}t}$
For figure of eight $\varnothing = 0,\pi,2\pi$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.