Conceptual question in regards to oscilloscope output

[claymine]

can some one help me understand this problem conceptually I'm doubting the explanation given below (superposition happens on when they are on the same axis right but this problem two frequencies are on orthogonal basis).
My thought was since frequency on Y is twice as many as on X. so i picked E

 

[claymine]

I plotted in mathematica for sin(x)+sin(2x)

 

[Dullard]

None of the choices are correct. (E) would be correct if the X/Y axis assignments in the problem statement are reversed.

 

[claymine]

None of the choices are correct. (E) would be correct if the X/Y axis assignments in the problem statement are reversed.

I agree with you. it's very stupid. but problem is it appeared on the 1992 GRE. so the problem maker might made a mistake

 

[claymine]

I agree with you. it's very stupid. but problem is it appeared on the 1992 GRE. so the problem maker might made a mistake

maybe if you zoom in you can get choice (A)

 

[Dullard]

LOL.
I was just pondering that. (A) is actually correct. A 90 degree phase shift will make the 'rotated' (E) look like (A).

 

[jrmichler]

Back in high school, a friend and I had playing privileges in the school physics room during the teacher's free hour. One day, we stacked up all the oscilloscopes and signal generators in a big pyramid, and connected them to make a different Lissajous figure on each scope. We were busy trying to make them all rotate clockwise (or something) when the principal walked in, looked at what we were doing, commented "gosh, that looks very technical", and went over and congratulated the teacher for doing a good job.

I just had to try this in Octave (Matlab clone). I made two plots, the top one with the signals in phase, and the bottom one where I added $\frac \pi 2$ to Y.

 

[claymine]

Back in high school, a friend and I had playing privileges in the school physics room during the teacher's free hour. One day, we stacked up all the oscilloscopes and signal generators in a big pyramid, and connected them to make a different Lissajous figure on each scope. We were busy trying to make them all rotate clockwise (or something) when the principal walked in, looked at what we were doing, commented "gosh, that looks very technical", and went over and congratulated the teacher for doing a good job.

I just had to try this in Octave (Matlab clone). I made two plots, the top one with the signals in phase, and the bottom one where I added $\frac \pi 2$ to Y.
View attachment 249309

wow bravo

 

[scottdave]

It's a parametric equation with x = function of t and y = function of t, like @jrmichler shows. It's tricky because they tell you it starts at the center of the screen. So you might think the figure 8. But with y having double frequency, it's slope will be steeper. My thinking, without a calculator or computer, first thought if they were same frequency you'd get something like a 45 degree line tracing back and forth. Now since y has the faster frequency, it would go up the entire vertical distance in the same time travel only half the horizontal distance. So the first choice is looking like it.