{"id":100292,"date":"2026-02-15T20:32:12","date_gmt":"2026-02-15T20:32:12","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100292"},"modified":"2026-02-15T20:32:12","modified_gmt":"2026-02-15T20:32:12","slug":"vibration-mount-selection","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/vibration-mount-selection\/","title":{"rendered":"\u0995\u09ae\u09cd\u09aa\u09a8 \u09ae\u09be\u0989\u09a8\u09cd\u099f \u09a8\u09bf\u09b0\u09cd\u09ac\u09be\u099a\u09a8 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0 | \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u09b8\u09b0\u099e\u09cd\u099c\u09be\u09ae #063"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Vibration Mount Selection Calculator\",\"alternateName\":[\"Anti-Vibration Mount Calculator\",\"Isolation Mount Selector\",\"Machine Mount Calculator\"],\"description\":\"Free online calculator for selecting vibration isolation mounts. Enter machine mass, operating frequency, and target isolation to determine required stiffness, number of mounts, and static deflection.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/vibration-mount-selection\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Mount stiffness calculation\",\"Natural frequency determination\",\"Static deflection\",\"Transmissibility analysis\",\"Auto-calculation on input change\",\"Multiple presets\"],\"keywords\":\"vibration mount, isolation, anti-vibration, stiffness, natural frequency, transmissibility\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"How do I select the right vibration mount?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Select vibration mounts based on the machine mass, operating frequency, and desired isolation percentage. The mount must have a natural frequency well below the disturbing frequency \u2014 typically fn \u2264 fd\/\u221a2 for any isolation, and fn \u2264 fd\/3 for 90% isolation.\"}},\n{\"@type\":\"Question\",\"name\":\"What isolation percentage should I target?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"For general machinery, 80-90% isolation is typical. For sensitive equipment near precision instruments, 95%+ is desired. The higher the isolation percentage, the softer (lower stiffness) the mounts must be, which increases static deflection.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the relationship between static deflection and natural frequency?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Natural frequency fn = (1\/2\u03c0)\u221a(g\/\u03b4st), where \u03b4st is static deflection and g is gravitational acceleration. A static deflection of ~25 mm gives fn \u2248 3.1 Hz. Softer mounts (more deflection) give lower natural frequency and better isolation.\"}},\n{\"@type\":\"Question\",\"name\":\"How many mounts should I use?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Typically 4 mounts for rectangular machines (one per corner). Use 3 for triangular arrangements, 6 for large machines or when load distribution is uneven. Each mount carries a fraction of the total load.\"}},\n{\"@type\":\"Question\",\"name\":\"What happens if mounts are too soft or too stiff?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Too stiff: insufficient isolation, vibration transmitted to the foundation. Too soft: excessive static deflection, potential instability, and amplification at resonance during startup\/shutdown. 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}\n    .vc-copy-btn, .vc-section-chevron, .vc-faq-chevron, .vc-presets, .vc-promo { display:none!important; }\n}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-vibration-mount-selection\">\n\n<!-- Header -->\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool #063<\/p>\n    <h1 class=\"vc-header-title\">Vibration Mount Selection Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Select vibration isolation mounts by machine mass, operating frequency, and target isolation percentage. Calculate required mount stiffness, number of mounts, and static deflection.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">Isolation Design<\/span>\n        <span class=\"vc-badge\">Transmissibility<\/span>\n        <span class=\"vc-badge\">Auto-Calc<\/span>\n    <\/div>\n<\/header>\n\n<!-- Calculator Card -->\n<div class=\"vc-card\">\n    <div class=\"vc-unit-bar\">\n        <button type=\"button\" class=\"vc-unit-btn vc-active\" data-system=\"metric\">Metric (kg, N\/mm, mm)<\/button>\n        <button type=\"button\" class=\"vc-unit-btn\" data-system=\"imperial\">Imperial (lb, lbf\/in, in)<\/button>\n    <\/div>\n\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-mass\">Machine Mass <span class=\"vc-label-hint\" id=\"vc-mass-unit\">(kg)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-mass\" inputmode=\"decimal\" step=\"any\" min=\"0.1\" placeholder=\"e.g. 500\" value=\"500\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-freq\">Operating Frequency <span class=\"vc-label-hint\">(Hz)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-freq\" inputmode=\"decimal\" step=\"any\" min=\"0.1\" placeholder=\"e.g. 25\" value=\"25\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-isolation\">Target Isolation <span class=\"vc-label-hint\">(%)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-isolation\" inputmode=\"decimal\" step=\"any\" min=\"50\" max=\"99.9\" placeholder=\"e.g. 90\" value=\"90\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-nmounts\">Number of Mounts<\/label>\n                <select class=\"vc-select\" id=\"vc-nmounts\">\n                    <option value=\"3\">3 mounts<\/option>\n                    <option value=\"4\" selected>4 mounts<\/option>\n                    <option value=\"6\">6 mounts<\/option>\n                    <option value=\"8\">8 mounts<\/option>\n                <\/select>\n            <\/div>\n        <\/div>\n\n        <!-- Presets -->\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-m=\"500\" data-f=\"25\" data-i=\"90\" data-n=\"4\">Pump 500 kg \/ 25 Hz<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-m=\"200\" data-f=\"50\" data-i=\"85\" data-n=\"4\">Motor 200 kg \/ 50 Hz<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-m=\"1500\" data-f=\"16.7\" data-i=\"95\" data-n=\"6\">Generator 1500 kg \/ 16.7 Hz<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-m=\"50\" data-f=\"100\" data-i=\"80\" data-n=\"4\">Compressor 50 kg \/ 100 Hz<\/button>\n        <\/div>\n    <\/form>\n\n    <!-- Results -->\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">Results<\/h2>\n            <button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">\n                <svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg>\n                Copy\n            <\/button>\n        <\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\">\n                <div class=\"vc-rcard-label\">Total Required Stiffness<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ktotal\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Stiffness per Mount<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-kmount\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Natural Frequency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-fn\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Static Deflection<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-defl\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Transmissibility<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-trans\">\u2014<\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Theory & Reference -->\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udcd8<\/span>\n            <span class=\"vc-section-title\">Theory &amp; Formulas<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner vc-theory\">\n            <h3>Transmissibility<\/h3>\n            <p>The transmissibility T defines the fraction of vibration force transmitted through the mounts:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <p>where r = f\/f<sub>n<\/sub> is the frequency ratio. For isolation (T &lt; 1), we need r &gt; \u221a2.<\/p>\n\n            <h3>Required Natural Frequency<\/h3>\n            <p>From the target isolation percentage, the required natural frequency is:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n\n            <h3>Required Stiffness<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n\n            <h3>Static Deflection<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-4\"><\/div>\n\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 Pump on 4 Mounts<\/div>\n                <p><strong>Given:<\/strong> Machine mass = 500 kg, Operating freq = 25 Hz, Target isolation = 90%, 4 mounts<\/p>\n                <p>T = 1 \u2212 0.90 = 0.10<\/p>\n                <p>r = \u221a(1\/T + 1) = \u221a(11) = 3.317<\/p>\n                <p>f<sub>n<\/sub> = 25 \/ 3.317 = 7.54 Hz<\/p>\n                <p>k<sub>total<\/sub> = m \u00d7 (2\u03c0f<sub>n<\/sub>)\u00b2 = 500 \u00d7 (2\u03c0 \u00d7 7.54)\u00b2 = <strong>1,122 kN\/m<\/strong><\/p>\n                <p>k<sub>per mount<\/sub> = 1122 \/ 4 = <strong>280.5 kN\/m \u2248 280.5 N\/mm<\/strong><\/p>\n                <p>Static deflection = mg\/k = 500 \u00d7 9.81 \/ 1,122,000 = <strong>4.37 mm<\/strong><\/p>\n            <\/div>\n\n            <div class=\"vc-warning-box\">\n                <p style=\"margin:0;font-size:14px;color:var(--vc-ink-secondary);\"><strong>\u26a0\ufe0f Note:<\/strong> This calculator assumes undamped single-degree-of-freedom isolation. Real mounts have damping that reduces resonance amplification but slightly reduces high-frequency isolation.<\/p>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Related Calculators -->\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udd17<\/span>\n            <span class=\"vc-section-title\">Related Calculators<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner\">\n            <div class=\"vc-related\">\n                <a class=\"vc-related-link\" href=\"\/calculators\/machine-vibration-isolation\/\">Machine Vibration Isolation<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/rubber-mount-calculator\/\">Rubber Mount Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/damping-ratio-calculator\/\">Damping Ratio Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/compression-spring-design\/\">Compression Spring Design<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/residual-unbalance-iso1940\/\">Residual Unbalance (ISO 1940)<\/a>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- FAQ -->\n<div class=\"vc-section\" id=\"vc-sec-faq\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\u2753<\/span>\n            <span class=\"vc-section-title\">Frequently Asked Questions<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner\">\n            <div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Promo -->\n<div class=\"vc-promo\">\n    <div class=\"vc-promo-text\">\n        <strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>\n        Professional field balancing instruments and software. Achieve optimal vibration isolation on-site. Used in 50+ countries.\n    <\/div>\n    <a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>\n<\/div>\n\n<!-- Footer -->\n<footer class=\"vc-footer\">\n    <p>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p>\n    <p style=\"font-size:12px;margin-top:4px;\">Vibration isolation design. Last updated: February 2025<\/p>\n    <div class=\"vc-footer-links\">\n        <a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a>\n        <a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a>\n    <\/div>\n<\/footer>\n\n<\/div>\n\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function() {\n    'use strict';\n\n    var SLUG = 'vibration-mount-selection';\n    var unitSystem = 'metric';\n\n    function $(id) { return document.getElementById(id); }\n    function fmt(n, d) { if(isNaN(n)||!isFinite(n)) return '\u2014'; var f=n.toFixed(d===undefined?2:d); return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,''); }\n\n    function calculate() {\n        var massVal = parseFloat($('vc-mass').value);\n        var freq = parseFloat($('vc-freq').value);\n        var isolation = parseFloat($('vc-isolation').value);\n        var nmounts = parseInt($('vc-nmounts').value);\n\n        if (!massVal || massVal <= 0 || !freq || freq <= 0 || !isolation || isolation <= 0 || isolation >= 100) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n\n        var massKg = unitSystem === 'imperial' ? massVal * 0.453592 : massVal;\n        var T = 1 - isolation \/ 100; \/\/ transmissibility\n        \/\/ T = 1\/(r\u00b2-1) for undamped, so r\u00b2 = 1\/T + 1\n        var r = Math.sqrt(1 \/ T + 1);\n        var fn = freq \/ r; \/\/ natural frequency Hz\n        var omega_n = 2 * Math.PI * fn;\n        var kTotal = massKg * omega_n * omega_n; \/\/ N\/m\n        var kPerMount = kTotal \/ nmounts;\n        var staticDefl = massKg * 9.81 \/ kTotal; \/\/ m\n\n        if (unitSystem === 'imperial') {\n            var kTotalImp = kTotal * 0.00571015; \/\/ N\/m to lbf\/in\n            var kMountImp = kPerMount * 0.00571015;\n            var deflIn = staticDefl * 39.3701;\n            $('vc-r-ktotal').innerHTML = fmt(kTotalImp, 1) + ' <span class=\"vc-rcard-unit\">lbf\/in<\/span>';\n            $('vc-r-kmount').innerHTML = fmt(kMountImp, 1) + ' <span class=\"vc-rcard-unit\">lbf\/in<\/span>';\n            $('vc-r-defl').innerHTML = fmt(deflIn, 3) + ' <span class=\"vc-rcard-unit\">in<\/span>';\n        } else {\n            var kTotalNmm = kTotal \/ 1000; \/\/ N\/mm\n            var kMountNmm = kPerMount \/ 1000;\n            var deflMm = staticDefl * 1000;\n            if (kTotalNmm >= 1000) {\n                $('vc-r-ktotal').innerHTML = fmt(kTotalNmm \/ 1000, 2) + ' <span class=\"vc-rcard-unit\">kN\/mm<\/span>';\n            } else {\n                $('vc-r-ktotal').innerHTML = fmt(kTotalNmm, 1) + ' <span class=\"vc-rcard-unit\">N\/mm<\/span>';\n            }\n            if (kMountNmm >= 1000) {\n                $('vc-r-kmount').innerHTML = fmt(kMountNmm \/ 1000, 2) + ' <span class=\"vc-rcard-unit\">kN\/mm<\/span>';\n            } else {\n                $('vc-r-kmount').innerHTML = fmt(kMountNmm, 1) + ' <span class=\"vc-rcard-unit\">N\/mm<\/span>';\n            }\n            $('vc-r-defl').innerHTML = fmt(deflMm, 2) + ' <span class=\"vc-rcard-unit\">mm<\/span>';\n        }\n\n        $('vc-r-fn').innerHTML = fmt(fn, 2) + ' <span class=\"vc-rcard-unit\">Hz<\/span>';\n        $('vc-r-trans').innerHTML = fmt(T * 100, 1) + ' <span class=\"vc-rcard-unit\">%<\/span> <span class=\"vc-rcard-unit\">(ratio ' + fmt(T, 4) + ')<\/span>';\n\n        $('vc-results').classList.add('vc-visible');\n\n        var u = new URL(window.location);\n        u.searchParams.set('mass', $('vc-mass').value);\n        u.searchParams.set('freq', freq);\n        u.searchParams.set('isolation', isolation);\n        u.searchParams.set('nmounts', nmounts);\n        history.replaceState(null, '', u.toString());\n\n        saveHistory({\n            mass: $('vc-mass').value, freq: freq, isolation: isolation, nmounts: nmounts,\n            _summary: 'm=' + $('vc-mass').value + (unitSystem === 'imperial' ? ' lb' : ' kg') + ', f=' + freq + ' Hz, ' + isolation + '% isolation'\n        });\n    }\n\n    \/* Unit toggle *\/\n    var unitBtns = document.querySelectorAll('.vc-unit-btn');\n    unitBtns.forEach(function(btn) {\n        btn.addEventListener('click', function() {\n            unitBtns.forEach(function(b) { b.classList.remove('vc-active'); });\n            this.classList.add('vc-active');\n            unitSystem = this.getAttribute('data-system');\n            $('vc-mass-unit').textContent = unitSystem === 'imperial' ? '(lb)' : '(kg)';\n            try { localStorage.setItem('vc_units', unitSystem); } catch(e) {}\n            calculate();\n        });\n    });\n\n    \/* Presets *\/\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn) {\n        btn.addEventListener('click', function(e) {\n            e.preventDefault();\n            var m = parseFloat(this.getAttribute('data-m'));\n            $('vc-mass').value = unitSystem === 'imperial' ? fmt(m * 2.20462, 1) : m;\n            $('vc-freq').value = this.getAttribute('data-f');\n            $('vc-isolation').value = this.getAttribute('data-i');\n            $('vc-nmounts').value = this.getAttribute('data-n');\n            calculate();\n        });\n    });\n\n    \/* Auto-calculate *\/\n    $('vc-form').addEventListener('input', calculate);\n    $('vc-form').addEventListener('change', calculate);\n\n    \/* Copy *\/\n    $('vc-copy-btn').addEventListener('click', function() {\n        var text = 'Vibration Mount Selection\\n' +\n            '\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\n' +\n            'Mass: ' + $('vc-mass').value + (unitSystem === 'imperial' ? ' lb' : ' kg') + '\\n' +\n            'Operating Freq: ' + $('vc-freq').value + ' Hz\\n' +\n            'Target Isolation: ' + $('vc-isolation').value + '%\\n' +\n            'Mounts: ' + $('vc-nmounts').value + '\\n' +\n            'Total Stiffness: ' + $('vc-r-ktotal').textContent + '\\n' +\n            'Per Mount: ' + $('vc-r-kmount').textContent + '\\n' +\n            'Natural Freq: ' + $('vc-r-fn').textContent + '\\n' +\n            'Static Deflection: ' + $('vc-r-defl').textContent + '\\n' +\n            '\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\n' +\n            'vibromera.eu\/calculators\/' + SLUG + '\/';\n        if (navigator.clipboard) {\n            navigator.clipboard.writeText(text).then(function() {\n                var btn = $('vc-copy-btn');\n                btn.classList.add('vc-copied');\n                btn.innerHTML = '<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';\n                setTimeout(function() {\n                    btn.classList.remove('vc-copied');\n                    btn.innerHTML = '<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy';\n                }, 2000);\n            });\n        }\n    });\n\n    \/* Collapsible sections *\/\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn) {\n        btn.addEventListener('click', function() {\n            var section = this.closest('.vc-section');\n            var isOpen = section.classList.contains('vc-open');\n            section.classList.toggle('vc-open');\n            this.setAttribute('aria-expanded', !isOpen);\n        });\n    });\n\n    \/* FAQ *\/\n    var faqData = [\n        { q: 'How do I select the right vibration mount?', a: '<p>Select vibration mounts based on the machine mass, operating frequency, and desired isolation percentage. The mount must have a natural frequency well below the disturbing frequency \u2014 typically f<sub>n<\/sub> \u2264 f<sub>d<\/sub>\/\u221a2 for any isolation, and f<sub>n<\/sub> \u2264 f<sub>d<\/sub>\/3 for 90% isolation.<\/p>' },\n        { q: 'What isolation percentage should I target?', a: '<p>For general machinery, 80\u201390% isolation is typical. For sensitive equipment near precision instruments, 95%+ is desired. Higher isolation requires softer mounts with more static deflection.<\/p>' },\n        { q: 'What is the relationship between static deflection and natural frequency?', a: '<p>Natural frequency f<sub>n<\/sub> = (1\/2\u03c0)\u221a(g\/\u03b4<sub>st<\/sub>), where \u03b4<sub>st<\/sub> is static deflection. A deflection of ~25 mm gives f<sub>n<\/sub> \u2248 3.1 Hz. Softer mounts = more deflection = lower f<sub>n<\/sub> = better isolation.<\/p>' },\n        { q: 'How many mounts should I use?', a: '<p>Typically 4 mounts for rectangular machines (one per corner). Use 3 for triangular arrangements, 6 for large machines or uneven load distribution. Each mount carries a fraction of the total load.<\/p>' },\n        { q: 'What happens if mounts are too soft or too stiff?', a: '<p><strong>Too stiff:<\/strong> Insufficient isolation, vibration transmitted to foundation.<br><strong>Too soft:<\/strong> Excessive static deflection, potential instability, and resonance amplification during startup\/shutdown. Mounts must support the load with acceptable deflection.<\/p>' }\n    ];\n    var faqList = $('vc-faq-list');\n    faqData.forEach(function(faq) {\n        faqList.innerHTML += '<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>' + faq.q + '<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">' + faq.a + '<\/div><\/div><\/div>';\n    });\n    faqList.addEventListener('click', function(e) {\n        var btn = e.target.closest('.vc-faq-q');\n        if (!btn) return;\n        btn.closest('.vc-faq-item').classList.toggle('vc-open');\n    });\n\n    \/* History *\/\n    function saveHistory(entry) {\n        var key = 'vc_history_' + SLUG;\n        var arr = [];\n        try { arr = JSON.parse(localStorage.getItem(key)) || []; } catch(e) {}\n        entry._ts = new Date().toISOString();\n        arr.unshift(entry);\n        if (arr.length > 10) arr = arr.slice(0, 10);\n        try { localStorage.setItem(key, JSON.stringify(arr)); 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