Free vibrations of an
elastic body, also called
natural vibrations, occur at the natural frequency. Natural vibrations are different from
forced 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 as
resonance where the system's response to the applied frequency is amplified.. A system's
normal mode is defined by the oscillation of a natural frequency in a
sine waveform. In analysis of systems, it is convenient to use the
angular frequency rather than the frequency
f, or the
complex frequency domain parameter . In a
mass–spring system, with mass
m and spring stiffness
k, the natural angular frequency can be calculated as: \omega _0 =\sqrt{\frac{k}{m}} In an
electrical network,
ω is a natural angular frequency of a response function
f(
t) if the
Laplace transform F(
s) of
f(
t) includes the term , where for a real
σ, and is a constant. Natural frequencies depend on network topology and element values but not their input. 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. A pole of the network
transfer 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. In
LC and
RLC circuits, its natural angular frequency can be calculated as: \omega _0 =\frac{1}{\sqrt{LC}} ==See also==