Natural frequency, also known as
eigenfrequency
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted ...
, 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
Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
in the absence of any driving force.
The motion pattern of a system oscillating at its natural frequency is called the
normal mode (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.
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 function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
.
In a
mass-spring system, with mass ''m'' and spring stiffness ''k'', the natural frequency can be calculated as:
In
electrical circuits
An electrical network is an interconnection of electrical components (e.g., batteries, resistors, inductors, capacitors, switches, transistors) or a model of such an interconnection, consisting of electrical elements (e.g., voltage sources, c ...
, ''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
Network topology is the arrangement of the elements ( links, nodes, etc.) of a communication network. Network topology can be used to define or describe the arrangement of various types of telecommunication networks, including command and contr ...
, 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
Mathematics ...
, ''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 m ...
or
current
Currents, Current or The Current may refer to:
Science and technology
* Current (fluid), the flow of a liquid or a gas
** Air current, a flow of air
** Ocean current, a current in the ocean
*** Rip current, a kind of water current
** Current (stre ...
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
In engineering, a transfer function (also known as system function or network function) of a system, sub-system, or component is a mathematical function that theoretically models the system's output for each possible input. They are widely used ...
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
An RLC circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), connected in series or in parallel. The name of the circuit is derived from the letters that are used to denote the constituent components ...
, 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. In ...
Footnotes
References
*
*
*
*
Waves
Oscillation
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