{"id":100166,"date":"2026-02-15T20:21:59","date_gmt":"2026-02-15T20:21:59","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100166"},"modified":"2026-07-12T22:47:34","modified_gmt":"2026-07-12T22:47:34","slug":"natural-frequency","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/sk\/calculators\/natural-frequency\/","title":{"rendered":"Linear SDOF Natural-Frequency Worksheet"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Linear SDOF Natural-Frequency Worksheet\",\"description\":\"Calculate undamped natural frequency for one documented linearized translational coordinate from effective mass and effective stiffness,with optional underdamped frequency and excitation-order speed crossing.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/natural-frequency\/\",\"applicationCategory\":\"Engineering Reference\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-12\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n<style>\n.nf-wrap{--ink:#17212b;--muted:#596775;--line:#d8e0e7;--soft:#f4f7f9;--blue:#1769aa;--blue2:#0f4f84;--warn:#fff7e5;max-width:980px;margin:0 auto;padding:20px 16px 46px;color:var(--ink);font:15px\/1.58 system-ui,-apple-system,\"Segoe UI\",sans-serif}.nf-wrap *{box-sizing:border-box}.nf-wrap [hidden]{display:none!important}.nf-hero{padding:38px 30px;border:1px solid var(--line);border-radius:18px;background:linear-gradient(135deg,#eef7ff,#fff 68%);box-shadow:0 10px 30px rgba(20,54,80,.07)}.nf-kicker{color:var(--blue);font-size:12px;font-weight:800;letter-spacing:.1em;text-transform:uppercase}.nf-hero h1{margin:8px 0 10px;font-size:clamp(27px,4vw,42px);line-height:1.12}.nf-lead{max-width:830px;margin:0;color:var(--muted);font-size:17px}.nf-badges{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px}.nf-badge{padding:5px 10px;border:1px solid #b9d4e8;border-radius:999px;background:#fff;color:var(--blue2);font-size:12px;font-weight:700}.nf-main{margin-top:20px}.nf-panel,.nf-section{border:1px solid var(--line);border-radius:14px;background:#fff;box-shadow:0 5px 18px rgba(23,33,43,.05)}.nf-panel{padding:24px}.nf-panel h2,.nf-section h2{margin:0 0 8px;font-size:21px}.nf-note{margin:0 0 18px;color:var(--muted)}.nf-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:16px}.nf-field{display:flex;flex-direction:column;gap:6px}.nf-wide{grid-column:1\/-1}.nf-label{font-weight:750}.nf-help{color:var(--muted);font-size:12px}.nf-input,.nf-select,.nf-textarea{width:100%;border:1.5px solid #bcc9d3;border-radius:8px;background:#fff;color:var(--ink);font:inherit;padding:10px 12px}.nf-textarea{min-height:100px;resize:vertical}.nf-input:focus,.nf-select:focus,.nf-textarea:focus{outline:3px solid rgba(23,105,170,.16);border-color:var(--blue)}.nf-error{min-height:24px;margin:14px 0 0;color:#a22727;font-weight:700}.nf-results{margin-top:20px;border:1px solid #b9d4e8;border-radius:12px;background:#f7fbff;padding:20px}.nf-rhead{display:flex;justify-content:space-between;gap:14px;align-items:flex-start}.nf-rtitle{font-size:19px;font-weight:800}.nf-rsub{max-width:620px;text-align:right;color:var(--muted);font-size:12px}.nf-rgrid{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:11px;margin-top:14px}.nf-card{padding:14px;border:1px solid #d7e5f0;border-radius:10px;background:#fff}.nf-card h3{margin:0 0 7px;color:var(--muted);font-size:12px;text-transform:uppercase;letter-spacing:.04em}.nf-val{font-size:20px;font-weight:800;overflow-wrap:anywhere}.nf-unit{margin-top:3px;color:var(--muted);font-size:11px}.nf-alert{margin-top:18px;padding:15px 17px;border:1px solid #e8cf91;border-radius:10px;background:var(--warn);color:#624b13}.nf-section{margin-top:18px;padding:22px 24px}.nf-section p{margin:8px 0;color:var(--muted)}.nf-section ul{margin:10px 0 0;padding-left:22px;color:var(--muted)}.nf-code{font-family:ui-monospace,SFMono-Regular,Consolas,monospace;color:#113d62}.nf-table{width:100%;border-collapse:collapse;margin-top:12px}.nf-table th,.nf-table td{padding:10px;border:1px solid var(--line);text-align:left;vertical-align:top}.nf-table th{background:var(--soft)}.nf-section a{color:var(--blue2)}@media(max-width:680px){.nf-grid,.nf-rgrid{grid-template-columns:1fr}.nf-wide{grid-column:auto}.nf-hero{padding:26px 20px}.nf-panel,.nf-section{padding:19px}.nf-rhead{display:block}.nf-rsub{text-align:left;margin-top:5px}}@media print{.nf-wrap{max-width:none}.nf-hero,.nf-panel,.nf-section{box-shadow:none}}\n<\/style>\n<div class=\"nf-wrap\">\n<header class=\"nf-hero\"><div class=\"nf-kicker\">One linearized coordinate \u00b7 effective properties \u00b7 no automatic resonance verdict<\/div><h1>Linear SDOF Natural-Frequency Worksheet<\/h1><p class=\"nf-lead\">Calculate the undamped natural frequency of one translational single-degree-of-freedom model from documented effective mass and stiffness. Optional damping and excitation order are evaluated separately;the result is not automatically a machine critical speed.<\/p><div class=\"nf-badges\"><span class=\"nf-badge\">\u03c9n=\u221a(k\/m)<\/span><span class=\"nf-badge\">Exact SI\/US conversions<\/span><span class=\"nf-badge\">No presets<\/span><span class=\"nf-badge\">Starts blank<\/span><\/div><\/header>\n<main class=\"nf-main\"><section class=\"nf-panel\"><h2>Define the linearized coordinate<\/h2><p class=\"nf-note\">Mass and stiffness must refer to the same displacement coordinate,direction,equilibrium\/preload and boundary conditions. For mounts or elastomers,use applicable dynamic\/tangent stiffness at the frequency,amplitude,temperature and preload of interest.<\/p><form id=\"nf-form\" novalidate><div class=\"nf-grid\">\n<div class=\"nf-field\"><label class=\"nf-label\" for=\"nf-mass\">Effective mass m<\/label><input class=\"nf-input\" id=\"nf-mass\" inputmode=\"decimal\" autocomplete=\"off\"><\/div>\n<div class=\"nf-field\"><label class=\"nf-label\" for=\"nf-mass-unit\">Mass unit<\/label><select class=\"nf-select\" id=\"nf-mass-unit\"><option value=\"\">Select\u2026<\/option><option value=\"kg\">kilogram (kg)<\/option><option value=\"lbm\">avoirdupois pound mass (lb)<\/option><\/select><\/div>\n<div class=\"nf-field\"><label class=\"nf-label\" for=\"nf-stiffness\">Effective stiffness k<\/label><input class=\"nf-input\" id=\"nf-stiffness\" inputmode=\"decimal\" autocomplete=\"off\"><\/div>\n<div class=\"nf-field\"><label class=\"nf-label\" for=\"nf-stiffness-unit\">Stiffness unit<\/label><select class=\"nf-select\" id=\"nf-stiffness-unit\"><option value=\"\">Select\u2026<\/option><option value=\"n-per-m\">N\/m<\/option><option value=\"n-per-mm\">N\/mm<\/option><option value=\"lbf-per-in\">lbf\/in<\/option><\/select><\/div>\n<div class=\"nf-field\"><label class=\"nf-label\" for=\"nf-damping\">Optional viscous damping ratio \u03b6<\/label><input class=\"nf-input\" id=\"nf-damping\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"nf-help\">Leave blank for undamped-only output;when entered,must satisfy0\u2264\u03b6&lt;1.<\/span><\/div>\n<div class=\"nf-field\"><label class=\"nf-label\" for=\"nf-order\">Optional documented excitation order q<\/label><input class=\"nf-input\" id=\"nf-order\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"nf-help\">For q cycles per revolution,the nominal speed crossing is60fn\/q.Not an automatic critical-speed decision.<\/span><\/div>\n<div class=\"nf-field nf-wide\"><label class=\"nf-label\" for=\"nf-coordinate\">Coordinate,configuration and boundary record<\/label><input class=\"nf-input\" id=\"nf-coordinate\" maxlength=\"600\" autocomplete=\"off\" placeholder=\"Translation coordinate\/direction;effective\/modal mass definition;support arrangement;preload\/equilibrium;constraints and boundaries\"><\/div>\n<div class=\"nf-field nf-wide\"><label class=\"nf-label\" for=\"nf-source\">Property\/source and applicability record<\/label><textarea class=\"nf-textarea\" id=\"nf-source\" maxlength=\"2400\" placeholder=\"Mass and stiffness source\/test\/model;dynamic versus static\/tangent stiffness;frequency\/amplitude\/preload\/temperature;uncertainty;damping method;excitation mechanism\/order and operating range\"><\/textarea><\/div>\n<\/div><p class=\"nf-error\" id=\"nf-error\" role=\"alert\"><\/p><\/form>\n<section class=\"nf-results\" id=\"nf-results\" hidden data-json=\"\"><div class=\"nf-rhead\"><div class=\"nf-rtitle\">Linear SDOF arithmetic<\/div><div class=\"nf-rsub\" id=\"nf-summary\">\u2014<\/div><\/div><div class=\"nf-rgrid\">\n<article class=\"nf-card\"><h3>Undamped natural frequency<\/h3><div class=\"nf-val\" id=\"nf-r-frequency\">\u2014<\/div><div class=\"nf-unit\">fn=\u03c9n\/(2\u03c0)<\/div><\/article>\n<article class=\"nf-card\"><h3>Undamped natural angular frequency<\/h3><div class=\"nf-val\" id=\"nf-r-omega\">\u2014<\/div><div class=\"nf-unit\">\u03c9n=\u221a(k\/m)<\/div><\/article>\n<article class=\"nf-card\"><h3>Undamped period<\/h3><div class=\"nf-val\" id=\"nf-r-period\">\u2014<\/div><div class=\"nf-unit\">Tn=1\/fn<\/div><\/article>\n<article class=\"nf-card\"><h3>Damped natural frequency<\/h3><div class=\"nf-val\" id=\"nf-r-damped\">\u2014<\/div><div class=\"nf-unit\">fd=fn\u221a(1\u2212\u03b6\u00b2);underdamped viscous model only<\/div><\/article>\n<article class=\"nf-card\"><h3>1\u00d7 cyclic-speed equivalent<\/h3><div class=\"nf-val\" id=\"nf-r-one-x\">\u2014<\/div><div class=\"nf-unit\">60fn;frequency conversion only<\/div><\/article>\n<article class=\"nf-card\"><h3>Entered-order speed crossing<\/h3><div class=\"nf-val\" id=\"nf-r-crossing\">\u2014<\/div><div class=\"nf-unit\">60fn\/q when q is documented<\/div><\/article>\n<article class=\"nf-card\"><h3>Effective mass in SI<\/h3><div class=\"nf-val\" id=\"nf-r-mass\">\u2014<\/div><div class=\"nf-unit\">same modeled coordinate<\/div><\/article>\n<article class=\"nf-card\"><h3>Effective stiffness in SI<\/h3><div class=\"nf-val\" id=\"nf-r-stiffness\">\u2014<\/div><div class=\"nf-unit\">same modeled coordinate<\/div><\/article>\n<article class=\"nf-card\"><h3>Coordinate record<\/h3><div class=\"nf-val\" id=\"nf-r-coordinate\">\u2014<\/div><div class=\"nf-unit\">verbatim evidence;not automatically interpreted<\/div><\/article>\n<\/div><\/section>\n<div class=\"nf-alert\"><strong>Decision boundary:<\/strong> this SDOF result does not establish a real machine&#8217;s complete modes,critical speeds,resonant amplitudes,separation margin or safe operating range. Multi-DOF\/continuous structures,rotor gyroscopic effects,bearing\/support dynamics,nonlinearity,damping,forcing order and speed-dependent properties require modal\/rotordynamic analysis or test.<\/div><\/section><\/main>\n<section class=\"nf-section\"><h2>Equations,units and scope<\/h2><table class=\"nf-table\"><thead><tr><th>Quantity<\/th><th>Equation<\/th><th>Applicability<\/th><\/tr><\/thead><tbody><tr><td>Undamped natural frequency<\/td><td><span class=\"nf-code\">m x\u00a8+kx=0<\/span><br><span class=\"nf-code\">\u03c9n=\u221a(k\/m)<\/span><br><span class=\"nf-code\">fn=\u03c9n\/(2\u03c0)<\/span><\/td><td>Linear translational SDOF about an equilibrium;positive effective m and k in the same coordinate.<\/td><\/tr><tr><td>Underdamped free frequency<\/td><td><span class=\"nf-code\">fd=fn\u221a(1\u2212\u03b6\u00b2)<\/span><\/td><td>Linear viscous damping with0\u2264\u03b6&lt;1.Not the forced-response peak in every response measure.<\/td><\/tr><tr><td>Excitation-order crossing<\/td><td><span class=\"nf-code\">n=60fn\/q<\/span><\/td><td>Only when q cycles\/revolution represents the documented forcing mechanism.<\/td><\/tr><\/tbody><\/table><p>Exact conversions used are1lb=0.45359237kg,1N\/mm=1000N\/m and1lbf\/in=175.12683524647638N\/m.The radian is dimensionless in these relations. Static deflection was removed because <span class=\"nf-code\">\u03b4=F\/k<\/span> needs an explicitly supported force,direction and the applicable static stiffness;it is not a universal output of any mass-stiffness pair.<\/p><\/section>\n<section class=\"nf-section\"><h2>Sources and standards boundary<\/h2><p><a href=\"https:\/\/ocw.mit.edu\/courses\/18-03-differential-equations-spring-2010\/88c76f911402d0605922fe9a1a9f36ea_MIT18_03S10_c13.pdf\" target=\"_blank\" rel=\"noopener\">MIT OpenCourseWare18.03,Class13<\/a> derives the linear mass-spring-damper equation,\u03c9n=\u221a(k\/m),and distinguishes the lower underdamped oscillation frequency. This is university mechanics,not an ISO formula.<\/p><p><a href=\"https:\/\/www.iso.org\/standard\/38937.html\" target=\"_blank\" rel=\"noopener\">ISO10846-2:2008,Edition2<\/a>,confirmed2022 and current,defines a laboratory direct method for dynamic transfer stiffness of resilient supports under specified preload. <a href=\"https:\/\/www.iso.org\/standard\/34561.html\" target=\"_blank\" rel=\"noopener\">ISO10846-4:2003,Edition1<\/a>,confirmed2023 and current,addresses dynamic transfer stiffness of other resilient elements for translation. Their scopes show why a catalogue static spring rate is not automatically the dynamic k of this model.Exact procedures and clauses beyond the public scopes are <span class=\"nf-code\">NEEDS_LICENSED_SOURCE<\/span>.<\/p><p>The <a href=\"https:\/\/www.bipm.org\/en\/publications\/si-brochure\/\" target=\"_blank\" rel=\"noopener\">BIPM SI Brochure,9th edition,updated2026<\/a> and exact international pound\/inch definitions provide the unit basis.Standard acceleration of free fall is9.80665m\/s\u00b2,but no gravity-derived deflection is calculated without an entered supported force.<\/p><\/section>\n<section class=\"nf-section\"><h2>Model safeguards<\/h2><ul><li>For a rigid machine translating on parallel mounts,k is the sum only if the mounts share that coordinate and the rigid-body\/equal-motion assumptions hold.Rotation,coupling and center-of-mass offset introduce more degrees of freedom.<\/li><li>Effective\/modal mass is coordinate and normalization dependent;total machine mass is not always the correct m.<\/li><li>Elastomer,pneumatic and hydraulic mount stiffness may depend on preload,frequency,amplitude,temperature and history.Use a compatible dynamic property.<\/li><li>Resonance is tied to forcing frequency,not shaft RPM alone.Excitation can occur at1\u00d7,blade\/vane pass,gear mesh,electromagnetic orders or transient sweeps.<\/li><li>No universal20\u201330% separation rule is applied.Acceptance needs applicable codes,manufacturer limits,uncertainty,damping\/response and all operating states.<\/li><\/ul><\/section>\n<section class=\"nf-section\"><h2>What was corrected<\/h2><p>The former page used the valid SDOF equation but prefilled generic machine presets,stored history\/units\/URL data,used rounded lb and lbf\/in conversions,reported <span class=\"nf-code\">60fn<\/span> as equivalent RPM without an excitation order,and advised a universal20\u201330% speed separation.It also reported <span class=\"nf-code\">mg\/k<\/span> static deflection for every model using rounded g=9.81.<\/p><p>The replacement starts blank,requires coordinate\/property evidence,uses exact conversions and strict point\/comma parsing,and labels the result as a linearized SDOF reference.Optional damping and excitation order are explicit inputs.Static deflection,presets,persistence,automatic resonance\/safety recommendations,prefix parsing and innerHTML were removed.<\/p><\/section>\n<\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var MASS={kg:1,lbm:0.45359237},STIFFNESS={'n-per-m':1,'n-per-mm':1000,'lbf-per-in':175.12683524647638};function num(s){s=String(s).trim();if(!s||s.includes('.')&&s.includes(',')||!\/^[+-]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;var n=Number(s.replace(',','.'));return Number.isFinite(n)&&Math.abs(n)<=1e100?n:NaN}function fmt(n){if(n===0)return'0';var a=Math.abs(n);return 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Zadajte hmotnos\u0165 a tuhos\u0165 pru\u017einy, aby ste z\u00edskali frekvenciu v Hz, uhlov\u00fa frekvenciu, peri\u00f3du a statick\u00fa v\u00fdchylku.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100166","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/calculator\/100166","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/calculator\/100166\/revisions"}],"predecessor-version":[{"id":102502,"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/calculator\/100166\/revisions\/102502"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/media?parent=100166"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/categories?post=100166"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/sk\/wp-json\/wp\/v2\/tags?post=100166"}],"curies":[{"name":"pracovn\u00fd list","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}