A 16-lb weight is placed upon the lower end of a coil spring suspended from the ceiling. At the equilibrium position, the spring stretches 24 inches. (a) Derive the differential equation that represents the above free undamped spring-mass system. (b) Find the equation of motion if the weight is pulled down 6 in. below its equilibrium position and released at t = 0 with an upward velocity of 2 ft/s. (c) Determine the amplitude, period and frequency of the resulting motion. (d) Now assume that the mass is attached to a dashpot damping device that offers a resistance force numerically equal to 8 times the instantaneous velocity. Determine the motion of the free damped mass- spring system with the same conditions stated in (b).