Natural frequency, also known as
eigenfrequency, is the
frequency
Frequency is the number of occurrences of a repeating event per unit of time. It is also occasionally referred to as ''temporal frequency'' for clarity, and is distinct from ''angular frequency''. Frequency is measured in hertz (Hz) which is eq ...
at which a system tends to
oscillate in the absence of any driving force.
The motion pattern of a system oscillating at its natural frequency is called the
normal mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. ...
(if all parts of the system move sinusoidally with that same frequency).
If the oscillating system is driven by an external force at the frequency at which the amplitude of its motion is greatest (close to a natural frequency of the system), this frequency is called
resonant frequency
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscilla ...
.
Overview
Free vibrations of an
elastic body are called ''natural vibrations'' and occur at a frequency called 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
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied periodic force (or a Fourier component of it) is equal or close to a natural frequency of the system on which it acts. When an oscil ...
.
In a
mass-spring system, with mass ''m'' and spring stiffness ''k'', the natural frequency can be calculated as:
In
electrical circuits, ''s
1'' is a natural frequency of variable ''x'' if the zero-input response of ''x'' includes the term
, where
is a constant dependent on initial state of the circuit,
network topology, and element values. In a
network
Network, networking and networked may refer to:
Science and technology
* Network theory, the study of graphs as a representation of relations between discrete objects
* Network science, an academic field that studies complex networks
Mathematic ...
, ''s
k'' is a natural frequency of the network if it is a natural frequency of some
voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
or
current in the network. Natural frequencies depend ''only'' on network topology and element values but not the 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. All poles of the network
transfer function are also natural frequencies of the corresponding response variable; however there may exist some natural frequencies that are not a pole of the network function. These frequencies happen at some special initial states.
In
LC and
RLC circuits, the natural frequency of a circuit can be calculated as:
See also
*
Fundamental frequency
The fundamental frequency, often referred to simply as the ''fundamental'', is defined as the lowest frequency of a periodic waveform. In music, the fundamental is the musical pitch of a note that is perceived as the lowest partial present. I ...
Footnotes
References
*
*
*
*
Waves
Oscillation
{{classicalmechanics-stub