{"id":64523,"date":"2025-05-12T10:05:23","date_gmt":"2025-05-12T07:05:23","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64523"},"modified":"2025-05-12T10:05:37","modified_gmt":"2025-05-12T07:05:37","slug":"spring-resonant-frequency","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/spring-resonant-frequency\/","title":{"rendered":"Spring Resonant Frequency Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 class=\"text-lg font-display font-bold\">Natural Frequency of Spring-Mass System<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"64523\" data-favorite-title=\"Spring Resonant Frequency\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/spring-resonant-frequency\/\" data-favorite-excerpt=\"This calculator determines the resonant frequency of a mass-spring system based on the mass and spring constant. It\u2019s essential for analyzing mechanical vibrations, oscillations, and tuning dynamic systems in engineering and physics.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-electrical\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/engineering\/spring-resonant-frequency\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64523\" data-post=\"64523\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Spring Constant<\/label><div class=\"term\">k<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"spring_constant\" id=\"field-1\" min=\"0.01\" step=\"0.01\" value=\"100\"\/><div class=\"unit\">N\/m<\/div><small>Spring stiffness or spring constant<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Mass<\/label><div class=\"term\">m<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"mass\" id=\"field-2\" min=\"0.001\" step=\"0.001\" value=\"2\"\/><div class=\"unit\">kg<\/div><small>Attached mass<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64523\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Resonant Frequency<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"Hz\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"64523\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform 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font-medium\">Disappointed <\/span><\/button><button class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">1<\/span><span class=\"reaction text-3xl\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<p><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Spring Resonant Frequency Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n$$f = \\frac{1}{2\\pi} \\cdot \\sqrt{\\frac{k}{m}}$$\n<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong><\/p>\n<ul>\n<li>$$f$$ = resonant frequency (Hz)  <\/li>\n<li>\n$$k$$ = spring constant (N\/m) <\/li>\n<li>$$m$$ = mass attached to the spring (kg)<\/li>\n<\/ul>\n<p>This formula assumes no damping and linear elastic behavior.<br \/>\r\n<\/section><br \/>\n<section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Spring Resonant Frequency \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<h3>Given:<\/h3>\n<ul>\n<li>$$k$$ = 200 N\/m  <\/li>\n<li>$$m$$ = 2 kg<\/li>\n<\/ul>\n<h3>Calculation:<\/h3>\n<ol>\n<li>$$f = \\frac{1}{2\\pi} \\cdot \\sqrt{\\frac{200}{2}} = \\frac{1}{6.283} \\cdot \\sqrt{100} = \\frac{1}{6.283} \\cdot 10 \u2248 1.59~\\text{Hz}$$<\/li>\n<\/ol>\n<p>\n\r\n<\/section><br \/>\nThe resonant frequency of a spring-mass system determines how fast it naturally oscillates when disturbed. This is a fundamental concept in mechanical engineering, acoustics, and vibration analysis. Knowing the natural frequency helps avoid resonance in structures, optimize damping, or deliberately tune systems for harmonic response, like in sensor or actuator design.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator determines the resonant frequency of a mass-spring system based on the mass and spring constant. It\u2019s essential for analyzing mechanical vibrations, oscillations, and tuning dynamic systems in engineering and physics.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[21],"class_list":["post-64523","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-electrical"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64523","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=64523"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64523\/revisions"}],"predecessor-version":[{"id":64526,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64523\/revisions\/64526"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64523"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64523"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64523"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}