# Lissajous figures circle problem

• negat1ve
In summary, the two inputs given by x = Asin(wt) and y = Acos(wt) would display a circle of radius A on the display of an oscilloscope. This is because in math theory, the x coordinate on the unit circle is cos(A) and the y coordinate is sin(A), where A = wt. This concept is known as Lissajous figures and can be researched further online.
negat1ve

## Homework Statement

Show that the two inputs given by x = Asin(wt) and y = Acos(wt) would display a circle of radius A on the display of an oscilloscope?

2*pi*f = w

This is a bonus lab question i am supposed to look online and research how to do but can't find anything that explains it well. Can anyone please help? Thanks!

Circles are pretty complicated. Have you ever seen that demo where a wheel is rolled along the ledge below the chalkboard and a piece of chalk on the turning wheel makes a graph on the board? That graph of its height is a sine wave.

In math theory, you always talk about the unit circle. The x coordinate on the unit circle is cos(A) and the y coord is sin(A), right? Imagine the point moving around the circle so its angle is A = wt. That should give you pretty much the same equations you were given for the scope.

The problem described is an example of Lissajous figures.Try googling.

## What are Lissajous figures?

Lissajous figures are complex curves that are created by the intersection of two harmonic motions. They are named after the French physicist Jules Antoine Lissajous who studied them in the 19th century.

## How are Lissajous figures created?

Lissajous figures are created by plotting the x and y coordinates of two harmonic motions against each other. The motions can be in the form of sine or cosine waves with different frequencies and phases.

## What is the purpose of studying Lissajous figures?

Lissajous figures have many applications in science and engineering, particularly in the fields of optics, electronics, and acoustics. They can be used to study and analyze the properties of oscillating systems and to create complex patterns for artistic and decorative purposes.

## What is the "circle problem" in relation to Lissajous figures?

The "circle problem" refers to the phenomenon where certain combinations of frequencies and phases of the harmonic motions used to create Lissajous figures result in a perfect circle. This is a special case of Lissajous figures and is of particular interest in mathematics and physics.

## Can Lissajous figures be used to visualize sound or music?

Yes, Lissajous figures can be used to visualize sound or music by connecting an audio signal to the input of an oscilloscope, which plots the signal as a Lissajous figure. This technique is often used in music concerts or audio demonstrations to create mesmerizing visualizations of sound waves in real-time.

• Introductory Physics Homework Help
Replies
3
Views
2K
• Introductory Physics Homework Help
Replies
7
Views
7K
• Introductory Physics Homework Help
Replies
43
Views
3K
• Introductory Physics Homework Help
Replies
16
Views
2K
• Engineering and Comp Sci Homework Help
Replies
6
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
21
Views
2K
• Introductory Physics Homework Help
Replies
1
Views
2K
• Introductory Physics Homework Help
Replies
2
Views
3K
• Calculus and Beyond Homework Help
Replies
3
Views
1K