resonans

Resonans, or resonance, is a physical phenomenon in which a system responds with unusually large amplitude to a periodic driving force when the forcing frequency coincides with one of the system's characteristic frequencies, known as the natural or resonant frequency. The strength of the response depends on how the system stores and dissipates energy, through properties such as stiffness, inertia, and damping.

In a simple damped harmonic oscillator described by m x'' + c x' + k x = F0 cos(ω t), the natural frequency is ω0 = sqrt(k/m). Damping reduces the peak, shifts the peak frequency to a value near ω0, and broadens the response. The steady-state amplitude is A(ω) = F0 / sqrt[(k − m ω^2)^2 + (c ω)^2].

Resonans appears across fields: mechanical resonance in structures and machinery; acoustic resonance in rooms and instruments; electrical resonance in LC circuits and antennas; optical resonance in cavities and nanosystems; and even in celestial mechanics where orbital resonances influence planetary motions.

Applications include frequency selection in tuning and filters, energy transfer efficiency in drivers and sensors, and design practices to avoid destructive resonance by adding damping, detuning, or isolation. Understanding resonans is essential for engineering, physics, and design.