Analyzing Lissajous Figures: Answer these questions about the last part assuming the function generators are always outputting sine waves.

Same Frequency, special cases: What do you expect to see if the two function generators are at exactly the same frequency and in-phase? What if they are out of phase (by 180 degrees)? What if they are 90 degrees out of phase?
Same Frequency, general case: In general, what do you expect to see if the two function generators are at exactly the same frequency with arbitrary phase?
Perfect n:m ratio: Suppose the two frequencies were exactly in an integer ratio (2:1, so one is twice the other; 3:2, so one is 3/2 of the other; etc.). What do you expect to see (as a static image) in this case? (Again, you may consider phase shift as well.)