Pure vertical displacement results in simple harmonic motion
When k is 10 times g, the motion looks much more regular
If we compress the spring extremely tightly, we can get some pretty unexpected paths. (The animation fails at this extreme)
Similar strengths of restorative force and gravity.
tldr; If you allow a mass on a spring to be displaced in 2 dimensions, the system is pretty neat! although there are no analytic equations of motion, we can use MATLAB to make pictures.