Lissajou's Figure: Name for Distorted Eight?

[Amith2006]

Homework Statement

When 2 simple harmonic motions are applied to a particle at right angles to each other having time periods in the ratio 1:2, you get a figure of eight. When the phase difference is (pi)/4,3(pi)/4,... you don't get a perfect figure of eight.Can it be called a distorted eight or is there any other name? I would like to follow the nomenclature that is universally accepted.That is why I asking.Thanx in advance.

Homework Equations

The Attempt at a Solution

 

[berkeman]

It's a 3-D rotating figure 8, isn't it? We used to put 60Hz into the horizontal of an oscilloscope and rock music into the vertical channel. Great stuff. Especially on the loud, hard bass guitar notes... Lots of rotating lissajou figures with fine treble detail fuzzing it all up...

 

[m2003]

The figure you are describing is commonly known as a Lissajous curve or Lissajous figure. These curves were first studied by French mathematician Jules Antoine Lissajous in the 19th century. The specific figure you are referring to, with a phase difference of (pi)/4,3(pi)/4,..., is known as a Lissajous figure with a ratio of 1:2.

While some may refer to this figure as a "distorted eight," it is more accurately described as a Lissajous figure with a specific ratio and phase difference. Lissajous figures are commonly used in physics and engineering to visualize the relationship between two different harmonic motions.

In terms of nomenclature, the name "Lissajous figure" is widely accepted and understood in the scientific community. If you are looking for a more specific term, you could refer to it as a "Lissajous figure with a ratio of 1:2 and a phase difference of (pi)/4,3(pi)/4,..."

I hope this helps clarify the terminology for you. Happy studying!