The performance of this physlet depends on computer processing speed. It works well on computers with ~500MHz processors, but traces may appear sporadic on faster machines.
The frequency ratios corresponding to these spring constant ratios are close to (but different from) rational fractions so the motion is not periodic. The slight shifting of the path with time gives the appearance of rotation in 3-space.
With the 1 to 0.98 ratio, simultaneous viewing of vx(t), vy(t), and the 2-d motion clearly show how the 2-d path depends on the phase difference between x and y motion.
Reference: Jerry B. Marion and Stephen T. Thornton, Classical Dynamics of Particles and Systems (4th edition, 1995) p. 111-114.
* This demonstration was written by Tim Gfroerer and scripted by Mario Belloni.