[From Bruce Abbott (2015.02.15.1200 EST)]
I’ve posted a revised version of my mass-spring-damper model on my Google site, Perceptual Control System Demos, where you can download it as a zip file. Find it at https://sites.google.com/site/perceptualcontroldemos/home/other-demos . After you unzip the file, just double-click the .exe file to run it. (The zip file also includes the Delphi source code and form specification, which are in text-file format.) As usual, this is a native Windows app but will run on a Mac with PC simulation.
The new version uses the revised code suggested by Rick Marken that gives the proper results when damping is set to zero. In addition, there is now a pair of “radio buttons” you can push to display position, velocity, and acceleration of the mass as a function of time (as the previous version did) or a phase plot showing velocity as a function of position. The latter produces a circle, centered around a point attractor, when damping is zero or a spiral that decays to the point attractor when damping is greater than zero. In either case the position of the point attractor shifts after the force pushing against the mass automatically switches off. (There is a slider control you can adjust to determine how long the force continues.)
Be aware that the model continues to execute, once started, until you click on the Reset button; you will need to do that if you wish to change system parameters for the next run.
This is the model that is used to simulate the springiness and velocity-dependent resistance to stretch of muscle + tendon in the motor-control simulations. It constitutes the environment side of a control-system model of motor control.