To make this all work, we have to do the animations separately, then combine them all into one plot at the end. We will use radius 1, but any value for the radius is fine. Now for the dot indicating the vertical position of the particle. This point also marks the position of a pen on a vertically oscillating spring. We need to describe the motion by finding a way to predict the position and velocity as functions of time.
Maple can take from here.
But it is the most general solution. Luckily, we can get Maple to a little more work that's interesting for physics, because we can give it information that is physically relevant. Maple allows us to put that information directly into dsolve. Both the spring constant and the mass are magnitudes, and therefore positive. Look at a plot to find out.