I believe the term Im looking for is phase diagram. For a oscillating system it is a graph where displacement is on the x-axis and velocity is on the y-axis. My first question is what is the proper name for this type of graph?

I had the following simple PDE: ay" + by' + cy = 0, just a run of the mill damped harmonic motion. To solve I split this up into two 1st order differential equations by the substitution v = y'. Then I basically used "dsolve" to find the y and v solutions. I then successfully plotted them against each other on my phase diagram to get the circular motion dying down towards zero.

Now my real problem starts. I want to plot velocity vs displacement VS time. So I will basically have a 3D version of what is happening. What this should look like is a spiral or spring, which gets more and more narrow as we progress in the z-axis, until it dies down and is just a vertical line along the z-axis. I was trying to use "plot3d" but could not get it to work.

Does anyone know how I can plot this in Maple? Please let me know if you need further clarification. Thank you.