Natural frequency, measured in terms ofeigenfrequency, is the rate at which an oscillatory system tends tooscillate in the absence of disturbance. A foundational example pertains tosimple harmonic oscillators, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency. The phenomenon ofresonance occurs when aforced vibration matches a system's natural frequency.
Free vibrations of anelastic body, also callednatural vibrations, occur at the natural frequency. Natural vibrations are different fromforced vibrations which happen at the frequency of an applied force (forced frequency). If the forced frequency is equal to the natural frequency, the vibrations' amplitude increases manyfold. This phenomenon is known asresonance where the system's response to the applied frequency is amplified..[1] A system'snormal mode is defined by the oscillation of a natural frequency in asine waveform.
In analysis of systems, it is convenient to use theangular frequencyω = 2πf rather than the frequencyf, or thecomplex frequency domain parameters =σ +ωi.
In amass–spring system, with massm and spring stiffnessk, the natural angular frequency can be calculated as:
In anelectrical network,ω is a natural angular frequency of a response functionf(t) if theLaplace transformF(s) off(t) includes the termKe−st, wheres =σ +ωi for a realσ, andK ≠ 0 is a constant.[2] Natural frequencies depend on network topology and element values but not their input.[3] It can be shown that the set of natural frequencies in a network can be obtained by calculating the poles of all impedance and admittance functions of the network.[4] A pole of the networktransfer function is associated with a natural angular frequencies of the corresponding response variable; however there may exist some natural angular frequency that does not correspond to a pole of the network function. These happen at some special initial states.[5]
InLC andRLC circuits, its natural angular frequency can be calculated as:[6]
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