The barrel of a field gun weighs 1800 lb and is returned into firing position after recoil by a recuperator of constant c = 1320 lb ⋅ s/ft. Determine

(a) The constant k which should be used for the recuperator to return the barrel into firing position in the shortest possible time without any oscillation,

(b) The time needed for the barrel to move back two-thirds of the way from its maximum-recoil position to its firing position.