A harmonic oscillator is a system that experiences a restoring force proportional to its displacement from an equilibrium position. This means that when the system is disturbed, it will oscillate back and forth around that position. Common examples include a mass on a spring or a pendulum. The motion is periodic, meaning it repeats at regular intervals. In physics, harmonic oscillators are important because they help describe various phenomena, such as sound waves and vibrations. The mathematical model of a harmonic oscillator is often used in fields like quantum mechanics, mechanical engineering, and electrical engineering to analyze systems that exhibit oscillatory behavior.