List of first-order theories: Difference between revisions
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'''Natural frequency''' is the frequency at which a system tends to [[oscillate]] in the absence of any driving or [[damping]] force.{{sfn|College|2012|p=569}} | |||
Free vibrations of any [[elastic body]] is called ''natural vibration'' and happens at a [[frequency]] called natural frequency. Natural vibrations are different from forced vibration 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]].{{sfn|Bhatt|p=122}} | |||
In [[electrical circuits]], ''s<sub>1</sub>'' is a natural frequency of variable ''x'', if the zero-input response of ''x'' includes the term <math>K_1 e^{-s_1t}</math> where <math>K_1 \neq 0</math> is a constant dependent on initial state of the circuit, [[network topology]], and element values.{{sfn|Desoer|1969|p=583-584}} In a [[Electrical network|network]], ''s<sub>k</sub>'' is a natural frequency of the network if it is a natural frequency of some [[voltage]] or [[current]] in the network.{{sfn|Desoer|1969|p=600}} Natural frequencies depend ''only'' on network topology and element values but not the input.{{sfn|Desoer|1969|p=633}} 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.{{sfn|Desoer|1969|p=635}} All poles of the network [[transfer function]] are also natural frequency 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.{{sfn|Desoer|1969|p=643}} | |||
In [[LC circuit|LC]] and [[RLC circuits]], natural frequency of circuit can be calculated as:{{sfn|Basic Physics|2009|p=366}} | |||
:<math>\omega _0 =\frac{1}{\sqrt{LC}}</math> | |||
== See also == | |||
* [[Fundamental frequency]] | |||
== References == | |||
{{reflist|2}} | |||
* {{cite book|last=Bhatt|first=P.|title=Maximum Marks Maximum Knowledge in Physics|publisher=Allied Publishers|isbn=9788184244441|url=http://books.google.com/books?id=eyFw4unYnhAC&pg=PA122|ref=harv|accessdate=2014-01-10}} | |||
* {{cite book|last=College|first=O.S.|title=College Physics|year=2012|url=http://books.google.com/books?id=pYpPAgAAQBAJ&pg=PA569|ref=harv|accessdate=2014-01-10}} | |||
* {{cite book|title=Basic Physics|publisher=Prentice-Hall Of India Pvt. Limited|year=2009|isbn=9788120337084|url=http://books.google.com/books?id=oS_vSI-3yuwC&pg=PA366|ref={{sfnref|Basic Physics|2009}}|accessdate=2014-01-10}} | |||
* {{cite book|last=Desoer|first=Charles|title=Basic circuit theory|publisher=McGraw-Hill|year=1969|isbn=0070165750|ref=harv|accessdate=2014-01-10}} | |||
[[Category:Waves]] | |||
[[Category:Oscillation]] | |||
{{classicalmechanics-stub}} | |||
Revision as of 19:12, 17 November 2013
Natural frequency is the frequency at which a system tends to oscillate in the absence of any driving or damping force.Template:Sfn
Free vibrations of any elastic body is called natural vibration and happens at a frequency called natural frequency. Natural vibrations are different from forced vibration 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.Template:Sfn
In electrical circuits, s1 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.Template:Sfn 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.Template:Sfn Natural frequencies depend only on network topology and element values but not the input.Template:Sfn 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.Template:Sfn All poles of the network transfer function are also natural frequency 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.Template:Sfn
In LC and RLC circuits, natural frequency of circuit can be calculated as:Template:Sfn
See also
References
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