Initial-Value Problems A 16-lb object is attached to the ceiling by a frictionless spring and stretches the spring 6 in. before coming to its equilibrium position. Formulate the initial-value problem describing the motion of the object under each of the following sets of conditions. Set x equal to the downward displacement from equilibrium.
(a) The object is pulled down 4 in. below its equilibrium position and released with an upward velocity of 4 ft/sec.
(b) The object is pushed up 2 in. and released with a downward velocity of I ft/sec.