Resonansrespons

Resonansrespons, or resonant response, refers to the behavior of a system when it is driven by a force or signal at a frequency close to the system’s natural frequency. At or near resonance, the system can exhibit larger oscillations than at other frequencies. The size and shape of the resonant response depend on the system’s mass, stiffness, damping, and geometrical properties.

In mechanical systems, a simple mass–spring–damper model has a natural (undamped) frequency ω0 = sqrt(k/m) and a damping ratio ζ = c/(2 sqrt(k m)). The resonance peak and the bandwidth of the response are governed by ζ: smaller damping yields a higher, narrower peak, while larger damping broadens the response and reduces peak amplitude. The frequency response can be described by how displacement or velocity responds to harmonic forcing across a range of frequencies, including the associated phase shift.

In electrical circuits, resonance occurs in RLC networks. A series RLC circuit resonates when the inductive and capacitive reactances cancel, yielding a minimal impedance; a parallel RLC circuit presents maximal impedance at resonance. The resonant frequency is f0 = 1/(2π sqrt(LC)). The quality factor Q and the bandwidth Δf = f0/Q characterize how sharp the resonance is.

Resonansrespons is typically analyzed using frequency response functions and impulse or step responses. It is central in designing systems to avoid unwanted amplification (such as in structures or machinery) or to exploit resonance (as in musical instruments, acoustics, or sensing).