Info about phase and frequency
How to use this site
Here is a quick breakdown of the different capabilities of this site
In this site you are able to change the fidelity, amplitude, frequency, period, and phase of two sinusoidal curves.
The factors that will have the largest impact on the Lissjous curve are the frequency, period, and phase.
Changing the frequency will change the ratio of the frequency's between the two curves which will in turn make the Lissajous figure appear more complex. Generally, even ratios like 1/4, 1/3, 1/5, 1/10 etc... will produce better looking curves than a ratio like 1/2.9934.
Changing the phase will change how the two curves are layered. If you press the play button on the phase slider, it will slowly increment the phase of one of the curves, and it will appear as if the Lissajous figure is rotating.
Changing the period will impact the number of oscillations of the curves that will be plotted. For high frequency curves I would recommend you make the period very small if you want to see a more zoomed in view of how the curves are interacting, or make the period larger to get a more complex and interesting shape.
Changing the amplitude will only change the range or domain of the Lissajous figure, and change the range of the superimposed plot.
Changing the fidelity of the plot will impact the number of points that the program will take of the curves. A higher fidelity will more accurately plot the curves, but will make the program run slower. A lower fidelity will plot faster, but will make a less accurate plot of the curves.
In this site you are able to change the fidelity, amplitude, frequency, period, and phase of two sinusoidal curves.
The factors that will have the largest impact on the Lissjous curve are the frequency, period, and phase.
Changing the frequency will change the ratio of the frequency's between the two curves which will in turn make the Lissajous figure appear more complex. Generally, even ratios like 1/4, 1/3, 1/5, 1/10 etc... will produce better looking curves than a ratio like 1/2.9934.
Changing the phase will change how the two curves are layered. If you press the play button on the phase slider, it will slowly increment the phase of one of the curves, and it will appear as if the Lissajous figure is rotating.
Changing the period will impact the number of oscillations of the curves that will be plotted. For high frequency curves I would recommend you make the period very small if you want to see a more zoomed in view of how the curves are interacting, or make the period larger to get a more complex and interesting shape.
Changing the amplitude will only change the range or domain of the Lissajous figure, and change the range of the superimposed plot.
Changing the fidelity of the plot will impact the number of points that the program will take of the curves. A higher fidelity will more accurately plot the curves, but will make the program run slower. A lower fidelity will plot faster, but will make a less accurate plot of the curves.
What are the graphs displayed?
A Lissajous curve is a visual representation of the interplay between two sinusoidal waves. It's formed by plotting the y-coordinate of one wave against the x-coordinate of the other, creating a distinct pattern that reveals information about the waves' relative frequency, phase, and amplitude.
There are two curves displayed on this site. The first is a lissajous curve. The second is a layering of the two sinusoidal curves on top of each other. The lissajous curve parametrically shows the relationship between the two curves, and the layering shows the functional relationship between the two curves.
For this site, the graph uses curve #1 for the x-coordinates of the lissajous figure, and curve #2 for the y-coordinates of the lissajous figure.
There are two curves displayed on this site. The first is a lissajous curve. The second is a layering of the two sinusoidal curves on top of each other. The lissajous curve parametrically shows the relationship between the two curves, and the layering shows the functional relationship between the two curves.
For this site, the graph uses curve #1 for the x-coordinates of the lissajous figure, and curve #2 for the y-coordinates of the lissajous figure.