Oscillation

Oscillation is repetitive motion or fluctuation about an equilibrium position. In physics, an oscillation is typically periodic, characterized by amplitude, period, frequency, and phase. The amplitude is the maximum displacement; the period is the time for one complete cycle; the frequency is the number of cycles per unit time (f = 1/T); the phase describes the position within the cycle at a given time.

Many oscillations can be described by simple harmonic motion when the restoring force is proportional to displacement, yielding x(t) = A cos(ω t + φ), with ω = 2π f. In the ideal case the energy alternates between kinetic and potential forms, and the total energy remains constant. Real systems exhibit damping, causing amplitude to fade, and may be driven by external forces, producing forced oscillations. When the driving frequency approaches the system's natural frequency, resonance can occur, producing large amplitudes.

Oscillations appear in diverse domains. Mechanical oscillators include pendulums and mass–spring systems; electrical oscillators include LC and RLC circuits; optical resonators support standing light waves; quantum systems show oscillatory evolution of states; biological rhythms such as circadian cycles are also oscillatory.

Applications span timekeeping, signal processing, acoustics, seismology, and instrumentation. The study of oscillations relies on differential equations, stability analysis, and Fourier methods to analyze frequency content and transient behavior. Early investigations by scientists such as Hooke and Huygens established foundational ideas, later extended by Fourier, Laplace, and others.