1. The problem statement, all variables and given/known data [URL]http://www2.seminolestate.edu/lvosbury/images/VibSpringAnNS.gif[/URL] Find the governing differential equation and position functions for a 32 pound object attached to the end of a spring with a spring constant of 1 and a forcing function that yields a constant velocity in the direction of motion. This velocity changes sign periodically. The forcing function is piecewise. The object is pulled down until the spring is stretched to 5 feet below its equilibrium position and then the object is released with an initial velocity of -1 ft/sec and the forcing function produces a constant velocity of -1 ft/sec. After the object has traveled 10 feet it is impeded and reverses direction with an initial velocity at that point of 1 ft/sec. and the forcing function changes to produce a constant velocity of 1 ft/sec. This behavior continues indefinitely. 2. Relevant equations 3. The attempt at a solution I am interested in only finding the piecewise function. I drew the graph. [URL]http://assets.openstudy.com/updates/attachments/4dfd29cf0b8bbe4f12e6e1ca-joseph20111-1308436975669-piecewise.bmp[/URL] I think I can use a calculator function such as frac(x) or int(x). I wrote a piecewise (unfinished) function that I believe can be simplified. [URL]http://assets.openstudy.com/updates/attachments/4dfd29cf0b8bbe4f12e6e1ca-joseph20111-1308447921585-pie.bmp[/URL] -t represents line with negative 1 slope. t represents line with positive 1 slope. I wrote (1)^n * t for alternating t. To write inequalities, 5 + 10n.