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Does anyone have a particular way of matching some of the more complicated circular functions to the pictures in the in-class sheet and test review? When the function combines linear and circular motion I find it easier to break them apart and visualize them, but I have more trouble picturing what is going on with the functions that compose a lot of circular motion, such as $\vec{p}(t) = 2\langle\cos(t), \sin(t), 0 \rangle + \langle \cos(t), \sin(t), 0\rangle + \langle 0, 0, 1\rangle \cos(22t)$. I am probably going to try to graph a lot of these in Mathematica or Woflram Alpha, but I was wondering if anyone had a particular way of visualizing these functions or determining what is going on with one.

Does anyone have a particular way of matching some of the more complicated circular functions to the pictures in the in-class sheet and test review? When the function combines linear and circular motion I find it easier to break them apart and visualize them, but I have more trouble picturing what is going on with the functions that compose a lot of circular motion, such as $\vec{p}(t) = 2\langle\cos(t), \sin(t), 0 \rangle + \langle \cos(t), \sin(t), 0\rangle + \langle 0, 0, 1\rangle \cos(22t)$. I am probably going to try to graph a lot of these in Mathematica or Woflram Alpha, but I was wondering if anyone had a particular way of visualizing these functions or determining what is going on with one.