A mass weighing 11lb stretches a spring 6in. The mass is attached to a viscous damper with damping constant 3lb*s/ft. The mass is pushed upward, contracting the spring a distance of 3in, and then set into motion with a downward velocity of 2in/s.
1. Determine the position u, in inches, of the mass at any time t. Use 32ft/s^2 as the acceleration due to gravity. Pay close attention to the units.