Oscillator

An oscillator is a system that produces periodic motion or signals by returning toward a center of rest after displacement or by using feedback to sustain repetition. Oscillators can be mechanical, electrical, or of other physical types, and they are foundational in timekeeping, communication, and signal processing.

In its simplest form a damped oscillator subject to a restoring force is described by an equation such as m d2x/dt2 + c dx/dt + k x = F(t), where x is displacement, k is stiffness, c is damping, and F(t) is an external drive. If F(t) = 0, the system is a free (natural) oscillator, whose motion decays due to damping. When driven by a periodic input, it becomes a forced oscillator and may exhibit stable, periodic responses at the drive frequency.

Key parameters include the natural frequency ω0 = sqrt(k/m), the damping ratio, and the quality factor Q, which measures how underdamped the system is and how sharp its resonance is. Mechanical examples include pendulums and mass-spring systems; electrical examples include resonant circuits such as LC tanks, RC oscillators, and crystal oscillators, which convert energy between electrical and magnetic or electric forms to sustain a stable periodic signal.

Relaxation oscillators, in contrast, produce non-sinusoidal waveforms (e.g., square or sawtooth waves) through nonlinear charging and discharging processes in circuits like astable multivibrators. In physics, the quantum harmonic oscillator models systems with a quadratic potential, yielding evenly spaced energy levels and fundamental insights into molecular vibrations and quantum fields.

Applications span clocks and time bases, radios and televisions, signal generation and processing, and precision timing in microprocessors and communication systems.