Math 307, mass-spring systems

Here are some graphs showing solutions to the second order equation 
    y'' + gy' + y = 0
(So g is the damping constant, instead of gamma, and the mass and spring constant are both 1: m=1 and k=1.)

Here is a picture showing the different sorts of equations: undamped, underdamped, critically damped, over damped.

In the underdamped case, the damping constant g is between 0 and 2; here are graphs for some of those values. Notice that as g increases and approaches 2, the oscillations decay more quickly, and also the frequency drops. underdamped solutions.

In the overdamped case, the damping constant g is bigger than 2; here are graphs for some of those values. There are no oscillations. As g increases, the graphs decay more slowly. overdamped solutions.

Questions or comments? E-mail me at palmieri@math.washington.edu.

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Last modified: Wed Nov 13 14:47:46 PST 2002