Which characteristic defines a simple harmonic oscillator?

A simple harmonic oscillator is defined by its motion that is both sinusoidal and characterized by a restoring force that is proportional to the displacement from an equilibrium position. This means that when the oscillator is displaced from its equilibrium point, there is a force that acts in the opposite direction, pulling it back toward the equilibrium. This behavior leads to periodic motion, which visually resembles sinusoidal waves.

The concept of a restoring force is crucial here. In simple harmonic motion, the magnitude of the restoring force depends linearly on how far the object is from the equilibrium position, following Hooke's Law (F = -kx, where k is a constant and x is the displacement). This relationship yields a motion pattern that oscillates back and forth around the equilibrium position, forming a classic sine or cosine wave when graphed over time.

The other characteristics mentioned do not define a simple harmonic oscillator. For example, an oscillator that follows linear motion would not exhibit the periodic behavior of a harmonic oscillator. Similarly, the motion in circles does not reflect the back and forth oscillation inherent to simple harmonic motion. Lastly, while some systems can have constant speed, simple harmonic oscillators do not; their speed varies, being maximum as they pass through equilibrium and zero at the extremes of