Solving perpendicular oscillation problems- lissajous

[SteveDB]

solving perpendicular oscillation problems-- lissajous

Hi all.
Ok, I am not getting how we're to solve perpendicular oscillatory systems.
How do the variances in frequency, and phase play into the drawing/solving of these systems?
Oh, and this is not a trig class I'm doing. It's an oscillation/wave class.
Do we solve for the individual trig functions, at various points in time, and mark our points within the rectangle, and then draw our lissajous graph?
Some serious clarification would be appreciated.
For what it's worth, I'm using the MIT Intro. Physics Series, A.P. French-- Vibrations and Waves text.
Thanks.

 

[quasar987]

How we're to solve them? Like we would two independant equations of motion (cuz that's what they are).

How to draw their Lissajous figure? Using the method explained thoroughly by French. If you don't understand it, tell me exactly where/what passage confuses you and I'll try to explain it better.

 

[quicknote]

Hello there,

Solving perpendicular oscillation problems, also known as Lissajous figures, involves understanding the relationship between two perpendicular oscillations. The variances in frequency and phase are important factors in determining the shape and pattern of the Lissajous figure.

To solve these problems, you can start by identifying the equations for the two perpendicular oscillations. These equations will involve trigonometric functions such as sine and cosine, as well as the frequencies and phases of the oscillations.

Next, you can plot points on a rectangular coordinate system using the values from the equations at different points in time. These points will form a pattern, which will eventually become the Lissajous figure.

The key to solving these problems is understanding the relationship between the two oscillations. For example, if the frequencies are the same, the Lissajous figure will be a straight line. If the frequencies are different, the figure will be a closed curve.

I understand that this may seem confusing, but with practice and a deeper understanding of trigonometric functions, you will be able to solve these problems easily. I recommend consulting your textbook and doing some practice problems to get a better grasp on the concepts.

I hope this helps. Keep up the good work in your oscillation/wave class!