This problem is an example of critically damped harmonic motion.

A hollow steel ball weighing 4 pounds is suspended from a spring.
This stretches the spring feet.
The ball is started in motion from the
equilibrium position
with a downward velocity of feet per second.
The air resistance (in pounds) of the moving ball
numerically equals 4 times its
velocity (in feet per second) .
Suppose that after t seconds the ball is y feet below its rest position.
Find y in terms of t.

Take as the gravitational acceleration 32 feet
per second per second. (Note that the positive y direction is down in this problem.)