Natural Frequency
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Natural Frequency

Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.[1]

## 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 frequency of applied force (forced frequency). If forced frequency is equal to the natural frequency, the amplitude of vibration increases manifold. This phenomenon is known as resonance.[2]

In a mass-spring system, with mass m and spring stiffness k, the natural frequency can be calculated as:

${\displaystyle \omega _{0}={\sqrt {\frac {k}{m}}}}$

In electrical circuits, s1 is a natural frequency of variable x if the zero-input response of x includes the term ${\displaystyle K_{1}e^{-s_{1}t}}$, where ${\displaystyle K_{1}\neq 0}$ is a constant dependent on initial state of the circuit, network topology, and element values.[3] In a network, sk is a natural frequency of the network if it is a natural frequency of some voltage or current in the network.[4] Natural frequencies depend only on network topology and element values but not the input.[5] 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.[6] 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.[7]

In LC and RLC circuits, the natural frequency of a circuit can be calculated as:[8]

${\displaystyle \omega _{0}={\frac {1}{\sqrt {LC}}}}$

## Footnotes

1. ^ College 2012, p. 569.
2. ^ Bhatt, p. 122.
3. ^ Desoer 1969, pp. 583-584.
4. ^ Desoer 1969, p. 600.
5. ^ Desoer 1969, p. 633.
6. ^ Desoer 1969, p. 635.
7. ^ Desoer 1969, p. 643.
8. ^ Basic Physics 2009, p. 366.

## References

• Bhatt, P. Maximum Marks Maximum Knowledge in Physics. Allied Publishers. ISBN 9788184244441. Retrieved 2014.
• College Physics. 2012. Retrieved 2014.
• Basic Physics. Prentice-Hall Of India Pvt. Limited. 2009. ISBN 9788120337084. Retrieved 2014.
• Desoer, Charles (1969). Basic circuit theory. McGraw-Hill. ISBN 0070165750.