Final answer:
The motion of a weight on a spring moving up and down with a velocity given by a cosine function is identified as simple harmonic motion, derived from the projection of uniform circular motion.
Step-by-step explanation:
The type of motion exhibited by a weight hung from a spring and moving up and down continuously, with the velocity given by v = 3cos(2πt), is simple harmonic motion (SHM). This kind of motion is characterized by a sinusoidal pattern in both velocity and displacement, with objects oscillating about an equilibrium position in a manner that is repetitive or periodic. The velocity expression given is indicative of harmonic motion, which is derived from the projection of uniform circular motion onto an axis. In uniform circular motion, an object travels on a circular path at a constant speed, with a centripetal acceleration directed towards the center of the circle due to a centripetal force. While the magnitude of velocity is constant, its direction changes continuously. On the other hand, in simple harmonic motion, the velocity and displacement follow sinusoidal functions, where the amplitude, frequency, and phase shift determine the specific motion characteristics.