What type of waveform does a simple mass on a spring produce?

A simple mass on a spring, when set in motion, behaves according to Hooke's Law, which states that the force exerted by the spring is proportional to the displacement of the mass from its equilibrium position. This results in simple harmonic motion, which is characterized by a restoring force that is directly proportional to the displacement.

The motion of a mass-spring system produces a smooth, continuous oscillation, resulting in a sinusoidal waveform. The sine wave reflects the periodic nature of the movement—where the mass travels through the maximum displacement in both directions (positive and negative) in a regular, repeating pattern over time. The attributes of a sine wave, such as the gradual rise and fall, align perfectly with the characteristics of a mass-spring system.

Understanding the nature of the mass-spring system and its relation to simple harmonic motion clarifies why the sine wave is the correct response. Other options, such as sawtooth, square, and triangle waves, have distinctly different shapes and behaviors associated with their formation, often depicting abrupt changes or linear characteristics, which are not present in the oscillatory motion of a mass on a spring.