A linear oscillator is a system that experiences periodic motion, where the restoring force is directly proportional to the displacement from its equilibrium position. This means that when the system is displaced, it will tend to return to its original position, creating a repetitive cycle of movement. Common examples include springs and pendulums, which follow the principles of Hooke's Law. Linear oscillators can be described mathematically using differential equations, often resulting in sinusoidal functions. These systems are fundamental in various fields, including mechanical engineering, electrical circuits, and quantum mechanics, where they help model behaviors like vibrations and waveforms.