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href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A7%8D%E0%A6%AC%E0%A6%BE%E0%A6%AD%E0%A6%BE%E0%A6%AC%E0%A6%BF%E0%A6%95_%E0%A6%95%E0%A6%AE%E0%A7%8D%E0%A6%AA%E0%A6%BE%E0%A6%99%E0%A7%8D%E0%A6%95" title="স্বাভাবিক কম্পাঙ্ক – Bangla" lang="bn" hreflang="bn" data-title="স্বাভাবিক কম্পাঙ্ক" data-language-autonym="বাংলা" data-language-local-name="Bangla" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A7%D0%B5%D1%81%D1%82%D0%BE%D1%82%D0%B0_%D0%BD%D0%B0_%D1%81%D0%BE%D0%B1%D1%81%D1%82%D0%B2%D0%B5%D0%BD%D0%B8%D1%82%D0%B5_%D1%82%D1%80%D0%B5%D0%BF%D1%82%D0%B5%D0%BD%D0%B8%D1%8F" title="Честота на собствените трептения – Bulgarian" lang="bg" hreflang="bg" data-title="Честота на собствените трептения" data-language-autonym="Български" data-language-local-name="Bulgarian" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-da 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class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Frecuencia_natural" title="Frecuencia natural – Spanish" lang="es" hreflang="es" data-title="Frecuencia natural" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%81%D8%B1%DA%A9%D8%A7%D9%86%D8%B3_%D8%B7%D8%A8%DB%8C%D8%B9%DB%8C" title="فرکانس طبیعی – Persian" lang="fa" hreflang="fa" data-title="فرکانس طبیعی" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Fr%C3%A9quence_propre" title="Fréquence propre – French" lang="fr" hreflang="fr" data-title="Fréquence propre" 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class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Frequency at which systems tend to oscillate</div> <p class="mw-empty-elt"> </p><p><b>Natural frequency</b>, measured in terms of <i><a href="/wiki/Eigenfrequency" class="mw-redirect" title="Eigenfrequency">eigenfrequency</a></i>, is the rate at which an oscillatory system tends to <a href="/wiki/Oscillate" class="mw-redirect" title="Oscillate">oscillate</a> in the absence of disturbance. A foundational example pertains to <a href="/wiki/Simple_harmonic_motion" title="Simple harmonic motion">simple harmonic oscillators</a>, such as an idealized spring with no energy loss wherein the system exhibits constant-amplitude oscillations with a constant frequency. The phenomenon of <a href="/wiki/Resonance" title="Resonance">resonance</a> occurs when a <a href="/wiki/Forced_vibration" class="mw-redirect" title="Forced vibration">forced vibration</a> matches a system's natural frequency. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Overview">Overview</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Natural_frequency&action=edit&section=1" title="Edit section: Overview"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Free_vibration" class="mw-redirect" title="Free vibration">Free vibrations</a> of an <a href="/wiki/Elastic_body" class="mw-redirect" title="Elastic body">elastic body</a>, also called <i>natural vibrations</i>, occur at the natural frequency. Natural vibrations are different from <a href="/wiki/Forced_vibration" class="mw-redirect" title="Forced vibration">forced vibrations</a> 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 <a href="/wiki/Resonance" title="Resonance">resonance</a>.<sup id="cite_ref-FOOTNOTEBhatt122_1-0" class="reference"><a href="#cite_note-FOOTNOTEBhatt122-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> A system's <i><a href="/wiki/Normal_mode" title="Normal mode">normal mode</a></i> is defined by the oscillation of a natural frequency in a <a href="/wiki/Sine_wave" title="Sine wave">sine waveform</a>. </p><p>In analysis of systems, it is convenient to use the <a href="/wiki/Angular_frequency" title="Angular frequency">angular frequency</a> <span class="nowrap"><i>ω</i> = 2<i>πf</i></span> rather than the frequency <i>f</i>, or the <a href="/wiki/Laplace_transform" title="Laplace transform">complex frequency domain parameter</a> <span class="nowrap"><i>s</i> = <i>σ</i> + <i>ω</i>i</span>. </p><p>In a <a href="/wiki/Simple_harmonic_motion#Mass_on_a_spring" title="Simple harmonic motion">mass–spring system</a>, with mass <i>m</i> and spring stiffness <i>k</i>, the natural angular frequency can be calculated as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{0}={\sqrt {\frac {k}{m}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mfrac> <mi>k</mi> <mi>m</mi> </mfrac> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{0}={\sqrt {\frac {k}{m}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4949e44f7e8b28b77faafce9c399525330d391d5" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:10.799ex; height:6.176ex;" alt="{\displaystyle \omega _{0}={\sqrt {\frac {k}{m}}}}"></span> </p><p>In an <a href="/wiki/Electrical_network" title="Electrical network">electrical network</a>, <i>ω</i> is a natural angular frequency of a response function <i>f</i>(<i>t</i>) if the <a href="/wiki/Laplace_transform" title="Laplace transform">Laplace transform</a> <i>F</i>(<i>s</i>) of <i>f</i>(<i>t</i>) includes the term <span class="nowrap"><i>Ke</i><sup>−<i>st</i></sup></span>, where <span class="nowrap"><i>s</i> = <i>σ</i> + <i>ω</i>i</span> for a real <i>σ</i>, and <span class="nowrap"><i>K</i> ≠ 0</span> is a constant.<sup id="cite_ref-FOOTNOTEDesoer1969583–584,_600_2-0" class="reference"><a href="#cite_note-FOOTNOTEDesoer1969583–584,_600-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Natural frequencies depend on network topology and element values but not their input.<sup id="cite_ref-FOOTNOTEDesoer1969633_3-0" class="reference"><a href="#cite_note-FOOTNOTEDesoer1969633-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> 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.<sup id="cite_ref-FOOTNOTEDesoer1969635_4-0" class="reference"><a href="#cite_note-FOOTNOTEDesoer1969635-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup> A pole of the network <a href="/wiki/Transfer_function" title="Transfer function">transfer function</a> 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.<sup id="cite_ref-FOOTNOTEDesoer1969643_5-0" class="reference"><a href="#cite_note-FOOTNOTEDesoer1969643-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>In <a href="/wiki/LC_circuit" title="LC circuit">LC</a> and <a href="/wiki/RLC_circuits" class="mw-redirect" title="RLC circuits">RLC circuits</a>, its natural angular frequency can be calculated as:<sup id="cite_ref-FOOTNOTEBasic_Physics2009366_6-0" class="reference"><a href="#cite_note-FOOTNOTEBasic_Physics2009366-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \omega _{0}={\frac {1}{\sqrt {LC}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ω</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>1</mn> <msqrt> <mi>L</mi> <mi>C</mi> </msqrt> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \omega _{0}={\frac {1}{\sqrt {LC}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d3719ddea03d2a499d44a142c1f0f68b5a98497c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.838ex; width:11.72ex; height:6.176ex;" alt="{\displaystyle \omega _{0}={\frac {1}{\sqrt {LC}}}}"></span> </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Natural_frequency&action=edit&section=2" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Fundamental_frequency" title="Fundamental frequency">Fundamental frequency</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Natural_frequency&action=edit&section=3" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist reflist-columns references-column-width" style="column-width: 30em;"> <ol class="references"> <li id="cite_note-FOOTNOTEBhatt122-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBhatt122_1-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBhatt">Bhatt</a>, p. 122.</span> </li> <li id="cite_note-FOOTNOTEDesoer1969583–584,_600-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDesoer1969583–584,_600_2-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDesoer1969">Desoer 1969</a>, pp. 583–584, 600.</span> </li> <li id="cite_note-FOOTNOTEDesoer1969633-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDesoer1969633_3-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDesoer1969">Desoer 1969</a>, p. 633.</span> </li> <li id="cite_note-FOOTNOTEDesoer1969635-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDesoer1969635_4-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDesoer1969">Desoer 1969</a>, p. 635.</span> </li> <li id="cite_note-FOOTNOTEDesoer1969643-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEDesoer1969643_5-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFDesoer1969">Desoer 1969</a>, p. 643.</span> </li> <li id="cite_note-FOOTNOTEBasic_Physics2009366-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEBasic_Physics2009366_6-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFBasic_Physics2009">Basic Physics 2009</a>, p. 366.</span> </li> </ol></div> <div class="mw-heading mw-heading3"><h3 id="Sources">Sources</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Natural_frequency&action=edit&section=4" title="Edit section: Sources"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFBhatt" class="citation book cs1">Bhatt, P. <a rel="nofollow" class="external text" href="https://books.google.com/books?id=eyFw4unYnhAC&pg=PA122"><i>Maximum Marks Maximum Knowledge in Physics</i></a>. Allied Publishers. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9788184244441" title="Special:BookSources/9788184244441"><bdi>9788184244441</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Maximum+Marks+Maximum+Knowledge+in+Physics&rft.pub=Allied+Publishers&rft.isbn=9788184244441&rft.aulast=Bhatt&rft.aufirst=P.&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DeyFw4unYnhAC%26pg%3DPA122&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANatural+frequency" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFBasic_Physics2009" class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=oS_vSI-3yuwC&pg=PA366"><i>Basic Physics</i></a>. Prentice-Hall of India Pvt. Limited. 2009. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9788120337084" title="Special:BookSources/9788120337084"><bdi>9788120337084</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Basic+Physics&rft.pub=Prentice-Hall+of+India+Pvt.+Limited&rft.date=2009&rft.isbn=9788120337084&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DoS_vSI-3yuwC%26pg%3DPA366&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANatural+frequency" class="Z3988"></span></li> <li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFDesoer1969" class="citation book cs1">Desoer, Charles (1969). <i>Basic circuit theory</i>. McGraw-Hill. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/0070165750" title="Special:BookSources/0070165750"><bdi>0070165750</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Basic+circuit+theory&rft.pub=McGraw-Hill&rft.date=1969&rft.isbn=0070165750&rft.aulast=Desoer&rft.aufirst=Charles&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANatural+frequency" class="Z3988"></span></li></ul> <div class="mw-heading mw-heading2"><h2 id="Further_reading">Further reading</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Natural_frequency&action=edit&section=5" title="Edit section: Further reading"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCollege_Physics2012" class="citation book cs1"><a rel="nofollow" class="external text" href="https://books.google.com/books?id=pYpPAgAAQBAJ&pg=PA569"><i>College Physics</i></a>. 2012.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=College+Physics&rft.date=2012&rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DpYpPAgAAQBAJ%26pg%3DPA569&rfr_id=info%3Asid%2Fen.wikipedia.org%3ANatural+frequency" class="Z3988"></span></li></ul> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output .hlist dt,.mw-parser-output .hlist li{margin:0;display:inline}.mw-parser-output .hlist.inline,.mw-parser-output .hlist.inline dl,.mw-parser-output .hlist.inline ol,.mw-parser-output .hlist.inline ul,.mw-parser-output .hlist dl dl,.mw-parser-output .hlist dl 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