Assignment:
A body that weighs 16 lb. is attached to the end of a spring which is stretched 2 ft. by a force of 100 lb. It is set in motion from a position of ½ foot from the equilibrium position of the spring with an initial velocity of -10 ft/sec. Assume the motion of this body is subject to a damping force that provides 6 lb of resistance to the motion for each foot per second of the body's velocity.
(a) Find the differential equation that governs the position of the body over time relative to the equilibrium position of the spring.
(b) Solve the differential equation.
Provide complete and step by step solution for the question and show calculations and use formulas.