An object of mass m = 40 grams attached to a coiled spring with damping factor b = 0.75 gram/second is pulled down a distance a = 15 centimeters from its rest position and then released. Assume that the positive direction of the motion is up and the period is T = 5 seconds under simple harmonic motion.

(a) Find a function that models the displacement d of the object from its rest position after t seconds.

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