Mechanical displacement

A steel ball weighing 128 pounds (mass= 4 slugs) is suspended from a spring. This stretches the spring  128/485 feet.

The ball is started in motion from the equilibrium position with a downward velocity of 9 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. (Note that this means that the positive direction for y is down.)

  

Take as the gravitational acceleration 32 feet per second per second.

When using English units (lb, ft, etc.) you need to be a bit careful with equations involving mass. Pounds (lb) is a unit of force, not mass. Using mg=F and g=32 ft/sec^2 we see that if an object weights L pounds it will have a mass of L/32 lb*sec^2/ft (or slugs).