Apple Newton Works Graphing Calculator - Manual (Page 26)

A 32-lb. weight is attached to the lower end of a coil spring suspended from the
ceiling. The weight comes to rest in its equilibrium position, stretching the spring
2 ft. The weight is then pulled down 5 in. below its equilibrium position and released
at t = 0. No external forces are present; but the resistance of the medium in pounds
is equal to 4(dx/dt), where dx/dt is the instantaneous velocity in feet per second. Plot
the damped oscillatory motion.
Using the above information with the basic differential equation for free,
damped motion:
m * d2x/dt2 + a * dx/dt + k * x = 0
Solving for the root and differentiating with respect to t, the solution is:
x = sqrt(3)/3 * e^(–2t) * cos(2sqrt(3) * t – /6)
26 Chapter 2