An object of mass m attached to a coiled spring with damping factor b is pulled down a distance a from its rest position and then released. Assume that the positive direction of the motion is up and the period is T under simple harmonic motion. 

(a) Develop a model that relates the distance d of the object from its rest position after t seconds. 

(b) Graph the equation found in part (a) for 5 oscillations. 

m = 40 grams; a = 15 centimeters; b = 0.75 gram/second; T = 5 seconds