Generalized Lissajous Figures

Rakesh Kumar Pandey

Kirori Mal College, University of Delhi

A simple extension in the graphical technique of drawing Lissajous Figures is proposed in this paper. It is shown how by making a simple modification in the way Lissajous figures are drawn, one can address the requirement of adding two Simple Harmonic Motions which are inclined at an arbitrary angle and are not necessarily perpendicular to each other. It is further added that such a discussion will not only generalize the understanding of superposition of SHMs within the undergraduate classroom teaching but also help the students in developing a clear understanding about the distinction between the ‘phase difference’ and ‘angle of inclination’ between two SHMs that is often encountered in the undergraduate students. As an invaluable extension, a condition is also derived in this paper to get a circular motion even when the two SHMs are not perpendicular.