{"id":100106,"date":"2026-02-15T20:16:52","date_gmt":"2026-02-15T20:16:52","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100106"},"modified":"2026-07-02T19:20:17","modified_gmt":"2026-07-02T19:20:17","slug":"foundation-vibration-from-machine","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/sw\/calculators\/foundation-vibration-from-machine\/","title":{"rendered":"Foundation Vibration from Machine | Transmitted Force"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Foundation Vibration from Machine Calculator\",\"alternateName\":[\"Transmitted Force Calculator\",\"Vibration Isolation Calculator\",\"Transmissibility Calculator\"],\"description\":\"Free online calculator for foundation vibration from machine unbalance. Computes transmitted force, transmissibility ratio, natural frequency, and isolation efficiency.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/foundation-vibration-from-machine\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2025-01-01\",\"dateModified\":\"2026-02-15\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Transmitted force calculation\",\"Transmissibility ratio\",\"Isolation efficiency\",\"Natural frequency\",\"Damping ratio support\",\"Auto-calculation\"],\"keywords\":\"foundation vibration, transmitted force, transmissibility, vibration isolation, natural frequency, damping\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is transmissibility in vibration isolation?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Transmissibility (T) is the ratio of transmitted force to the disturbing force. T < 1 means isolation is effective (force is reduced). T > 1 means the mount amplifies vibration, which happens near resonance. Effective isolation requires operating well above the natural frequency (frequency ratio r > \u221a2 \u2248 1.414).\"}},\n{\"@type\":\"Question\",\"name\":\"How do I choose the right mount stiffness?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The mount stiffness determines the system natural frequency. For effective isolation, the natural frequency should be at least 2.5\u20134\u00d7 lower than the machine operating frequency. Lower stiffness = lower natural frequency = better isolation, but too soft causes excessive static deflection and instability.\"}},\n{\"@type\":\"Question\",\"name\":\"What is a typical damping ratio for machine mounts?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Typical damping ratios: rubber mounts \u03b6 \u2248 0.03\u20130.10, spring isolators \u03b6 \u2248 0.01\u20130.03, air springs \u03b6 \u2248 0.02\u20130.05. Higher damping reduces resonance amplification but slightly reduces high-frequency isolation efficiency.\"}},\n{\"@type\":\"Question\",\"name\":\"Why does adding foundation mass help reduce vibration?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Increasing total mass (machine + foundation) lowers the natural frequency for the same stiffness, increasing the frequency ratio. This moves the system further above resonance, improving isolation. A heavier foundation is also harder to accelerate, reducing vibration amplitude directly.\"}},\n{\"@type\":\"Question\",\"name\":\"What happens at resonance (frequency ratio r = 1)?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"At resonance, the transmissibility peaks dramatically. With low damping (\u03b6 = 0.05), T can exceed 10\u00d7 \u2014 meaning the transmitted force is 10 times the disturbing force. This is why machines must never operate at or near their mount natural frequency. During run-up\/coast-down, passing through resonance briefly is managed by increasing damping.\"}}\n]}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[\n{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},\n{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},\n{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Foundation Vibration Calculator\",\"item\":\"https:\/\/vibromera.eu\/calculators\/foundation-vibration-from-machine\/\"}\n]}\n<\/script>\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\n\n<link rel=\"preconnect\" href=\"https:\/\/fonts.gstatic.com\" crossorigin>\n\n<link 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class=\"vc-badge\">Transmissibility<\/span>\n        <span class=\"vc-badge\">Isolation Efficiency<\/span>\n        <span class=\"vc-badge\">Natural Frequency<\/span>\n    <\/div>\n<\/header>\n\n<div class=\"vc-card\">\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-mmachine\">Machine Mass <span class=\"vc-label-hint\">(kg)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-mmachine\" inputmode=\"decimal\" step=\"any\" min=\"0.001\" placeholder=\"e.g. 500\" value=\"500\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-unbalance\">Unbalance <span class=\"vc-label-hint\">(g\u00b7mm)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-unbalance\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 3000\" value=\"3000\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-speed\">Speed <span class=\"vc-label-hint\">(RPM)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-speed\" inputmode=\"decimal\" step=\"any\" min=\"1\" placeholder=\"e.g. 3000\" value=\"3000\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-mfound\">Foundation Mass <span class=\"vc-label-hint\">(kg)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-mfound\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 2000\" value=\"2000\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-stiffness\">Total Mount Stiffness k <span class=\"vc-label-hint\">(N\/mm)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-stiffness\" inputmode=\"decimal\" step=\"any\" min=\"0.001\" placeholder=\"e.g. 5000\" value=\"5000\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-damping\">Damping Ratio \u03b6 <span class=\"vc-label-hint\">(default 0.05)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-damping\" inputmode=\"decimal\" step=\"any\" min=\"0\" max=\"1\" placeholder=\"e.g. 0.05\" value=\"0.05\">\n            <\/div>\n        <\/div>\n\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-mm=\"500\" data-u=\"3000\" data-s=\"3000\" data-mf=\"2000\" data-k=\"5000\" data-z=\"0.05\">Fan 500kg, 3000g\u00b7mm, 3000RPM, 2000kg, k=5000<\/button>\n        <\/div>\n    <\/form>\n\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\">Transmitted Force to Foundation<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ftrans\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Transmissibility Ratio T<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-trans\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Frequency Ratio r = \u03c9\/\u03c9_n<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-ratio\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Natural Frequency f_n<\/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\">Unbalance Force F_unbal<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-funbal\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Isolation Efficiency<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-eff\">\u2014<\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Theory -->\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>Unbalance Force<\/h3>\n            <p>The centrifugal force generated by the machine unbalance:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n\n            <h3>Natural Frequency<\/h3>\n            <p>The natural frequency of the machine-foundation system on mounts:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <p>Where k is total mount stiffness (N\/mm \u00d7 1000 \u2192 N\/m), and m<sub>total<\/sub> = m<sub>machine<\/sub> + m<sub>foundation<\/sub>.<\/p>\n\n            <h3>Transmissibility<\/h3>\n            <p>The ratio of transmitted force to disturbing force, including damping:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n            <ul>\n                <li><strong>r<\/strong> = \u03c9\/\u03c9<sub>n<\/sub> \u2014 frequency ratio<\/li>\n                <li><strong>\u03b6<\/strong> \u2014 damping ratio (dimensionless)<\/li>\n                <li><strong>T &lt; 1<\/strong> \u2014 isolation is effective<\/li>\n                <li><strong>T &gt; 1<\/strong> \u2014 amplification (near resonance)<\/li>\n            <\/ul>\n\n            <h3>Isolation Efficiency<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-4\"><\/div>\n\n            <h3>Practical Example<\/h3>\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 Fan on Concrete Foundation<\/div>\n                <p><strong>Given:<\/strong> Machine 500 kg, Unbalance 3000 g\u00b7mm, 3000 RPM, Foundation 2000 kg, k = 5000 N\/mm, \u03b6 = 0.05<\/p>\n                <p>\u03c9 = 2\u03c0 \u00d7 3000 \/ 60 = 314.16 rad\/s<\/p>\n                <p>F<sub>unbal<\/sub> = 3000 \/ 1e6 \u00d7 314.16\u00b2 = <strong>296.1 N<\/strong><\/p>\n                <p>\u03c9<sub>n<\/sub> = \u221a(5,000,000 \/ 2500) = 44.72 rad\/s \u2192 f<sub>n<\/sub> = 7.12 Hz<\/p>\n                <p>r = 314.16 \/ 44.72 = 7.02<\/p>\n                <p>T = \u221a(1 + (2\u00d70.05\u00d77.02)\u00b2) \/ \u221a((1 \u2212 7.02\u00b2)\u00b2 + (2\u00d70.05\u00d77.02)\u00b2) \u2248 0.0253<\/p>\n                <p>F<sub>transmitted<\/sub> = 296.1 \u00d7 0.0253 = <strong>7.5 N<\/strong><\/p>\n                <p>Isolation efficiency = (1 \u2212 0.0253) \u00d7 100% = <strong>97.5%<\/strong><\/p>\n            <\/div>\n\n            <div class=\"vc-info-box\">\n                <p><strong>\ud83d\udca1 Tip:<\/strong> For effective isolation, aim for a frequency ratio r > 3 (isolation efficiency > 88%). This means the natural frequency should be at least 3\u00d7 lower than the operating frequency.<\/p>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Related -->\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\/residual-unbalance-iso1940\/\">Residual Unbalance (ISO 21940)<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/fan-blade-centrifugal-force\/\">Fan Blade Centrifugal Force<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/vibration-velocity\/\">Vibration Velocity (ISO 10816)<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/propeller-unbalance\/\">Propeller Unbalance<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/separator-balancing\/\">Separator Balancing<\/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<div class=\"vc-promo\">\n    <div class=\"vc-promo-text\">\n        <strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>\n        Professional vibration analysis instruments for foundation and machine diagnostics. Identify unbalance, misalignment, and resonance on-site.\n    <\/div>\n    <a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>\n<\/div>\n\n<footer class=\"vc-footer\">\n    <p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p>\n    <p style=\"font-size:12px;margin-top:4px;\">Calculator #243. Last updated: February 2026<\/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    var SLUG = 'foundation-vibration-from-machine';\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 mMachine = parseFloat($('vc-mmachine').value);\n        var U = parseFloat($('vc-unbalance').value);\n        var speed = parseFloat($('vc-speed').value);\n        var mFound = parseFloat($('vc-mfound').value);\n        var k = parseFloat($('vc-stiffness').value);\n        var zeta = parseFloat($('vc-damping').value);\n\n        if (!mMachine || mMachine <= 0 || !speed || speed <= 0 || !k || k <= 0) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n        if (isNaN(U) || U < 0) U = 0;\n        if (isNaN(mFound) || mFound < 0) mFound = 0;\n        if (isNaN(zeta) || zeta < 0) zeta = 0.05;\n\n        var omega = 2 * Math.PI * speed \/ 60;\n        var Funbal = U \/ 1e6 * omega * omega; \/\/ N\n\n        var mTotal = mMachine + mFound;\n        var kSI = k * 1000; \/\/ N\/m\n        var omega_n = Math.sqrt(kSI \/ mTotal);\n        var fn = omega_n \/ (2 * Math.PI);\n\n        var r = omega \/ omega_n;\n        var r2 = r * r;\n        var zr2 = 2 * zeta * r;\n\n        \/\/ Transmissibility\n        var num = Math.sqrt(1 + zr2 * zr2);\n        var den = Math.sqrt((1 - r2) * (1 - r2) + zr2 * zr2);\n        var T = num \/ den;\n\n        var Ftrans = Funbal * T;\n        var efficiency = T < 1 ? (1 - T) * 100 : 0;\n\n        $('vc-r-ftrans').innerHTML = fmt(Ftrans, Ftrans < 1 ? 3 : 1) + ' <span class=\"vc-rcard-unit\">N<\/span>';\n        $('vc-r-trans').innerHTML = fmt(T, 4);\n        $('vc-r-ratio').innerHTML = fmt(r, 2);\n        $('vc-r-fn').innerHTML = fmt(fn, 2) + ' <span class=\"vc-rcard-unit\">Hz<\/span> <span class=\"vc-rcard-unit\">(' + fmt(omega_n, 1) + ' rad\/s)<\/span>';\n        $('vc-r-funbal').innerHTML = fmt(Funbal, 1) + ' <span class=\"vc-rcard-unit\">N<\/span>';\n\n        if (T < 1) {\n            $('vc-r-eff').innerHTML = fmt(efficiency, 1) + ' <span class=\"vc-rcard-unit\">%<\/span>';\n        } else {\n            $('vc-r-eff').innerHTML = '<span style=\"color:var(--vc-red)\">Amplification (' + fmt(T, 2) + '\u00d7)<\/span>';\n        }\n\n        $('vc-results').classList.add('vc-visible');\n\n        var u = new URL(window.location);\n        u.searchParams.set('mmachine', mMachine); u.searchParams.set('unbalance', U);\n        u.searchParams.set('speed', speed); u.searchParams.set('mfound', mFound);\n        u.searchParams.set('stiffness', k); u.searchParams.set('damping', zeta);\n        history.replaceState(null, '', u.toString());\n\n        saveHistory({ mmachine:mMachine, unbalance:U, speed:speed, mfound:mFound, stiffness:k, damping:zeta,\n            _summary: mMachine + 'kg, U=' + U + 'g\u00b7mm, ' + speed + 'RPM, k=' + k + 'N\/mm' });\n    }\n\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn) {\n        btn.addEventListener('click', function(e) {\n            e.preventDefault();\n            $('vc-mmachine').value = this.getAttribute('data-mm');\n            $('vc-unbalance').value = this.getAttribute('data-u');\n            $('vc-speed').value = this.getAttribute('data-s');\n            $('vc-mfound').value = this.getAttribute('data-mf');\n            $('vc-stiffness').value = this.getAttribute('data-k');\n            $('vc-damping').value = this.getAttribute('data-z');\n            calculate();\n        });\n    });\n\n    $('vc-form').addEventListener('input', calculate);\n    $('vc-form').addEventListener('change', calculate);\n\n    $('vc-copy-btn').addEventListener('click', function() {\n        var text = 'Foundation Vibration Calculation\\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            'Machine Mass: ' + $('vc-mmachine').value + ' kg\\n' +\n            'Unbalance: ' + $('vc-unbalance').value + ' g\u00b7mm\\n' +\n            'Speed: ' + $('vc-speed').value + ' RPM\\n' +\n            'Foundation Mass: ' + $('vc-mfound').value + ' kg\\n' +\n            'Stiffness: ' + $('vc-stiffness').value + ' N\/mm\\n' +\n            'Damping \u03b6: ' + $('vc-damping').value + '\\n' +\n            'Transmitted Force: ' + $('vc-r-ftrans').textContent + '\\n' +\n            'Transmissibility: ' + $('vc-r-trans').textContent + '\\n' +\n            'Frequency Ratio: ' + $('vc-r-ratio').textContent + '\\n' +\n            'Natural Frequency: ' + $('vc-r-fn').textContent + '\\n' +\n            'Isolation Efficiency: ' + $('vc-r-eff').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\/foundation-vibration-from-machine\/';\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() { btn.classList.remove('vc-copied'); 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'; }, 2000);\n            });\n        }\n    });\n\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn) {\n        btn.addEventListener('click', function() {\n            var section = this.closest('.vc-section');\n            section.classList.toggle('vc-open');\n            this.setAttribute('aria-expanded', section.classList.contains('vc-open'));\n        });\n    });\n\n    var faqData = [\n        { q: 'What is transmissibility in vibration isolation?', a: '<p>Transmissibility (T) is the ratio of transmitted force to the disturbing force. When T < 1, isolation is effective. When T > 1 (near resonance), the mount actually amplifies vibration. Effective isolation requires the operating speed to be well above the mount natural frequency (r > \u221a2 \u2248 1.414).<\/p>' },\n        { q: 'How do I choose the right mount stiffness?', a: '<p>Mount stiffness determines the natural frequency. For effective isolation, the natural frequency should be 2.5\u20134\u00d7 lower than the machine operating frequency. Lower stiffness gives better isolation but increases static deflection. A balance must be struck between isolation and stability.<\/p>' },\n        { q: 'What is a typical damping ratio for machine mounts?', a: '<p>Typical values:<\/p><ul><li><strong>Rubber mounts:<\/strong> \u03b6 \u2248 0.03\u20130.10<\/li><li><strong>Spring isolators:<\/strong> \u03b6 \u2248 0.01\u20130.03<\/li><li><strong>Air springs:<\/strong> \u03b6 \u2248 0.02\u20130.05<\/li><\/ul><p>Higher damping reduces resonance peaks but slightly reduces high-frequency isolation efficiency.<\/p>' },\n        { q: 'Why does adding foundation mass help reduce vibration?', a: '<p>Increasing total mass lowers the natural frequency for the same stiffness, increasing the frequency ratio r. This improves isolation. A heavier foundation is also harder to accelerate, reducing vibration amplitude directly. Inertia blocks serve this purpose.<\/p>' },\n        { q: 'What happens at resonance (frequency ratio r = 1)?', a: '<p>At resonance, transmissibility peaks dramatically. With \u03b6 = 0.05, T can exceed 10\u00d7 \u2014 the transmitted force is 10 times the disturbing force. Machines must never operate at or near their mount natural frequency. Pass through resonance quickly during start-up\/shut-down.<\/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) { var btn = e.target.closest('.vc-faq-q'); if (!btn) return; btn.closest('.vc-faq-item').classList.toggle('vc-open'); });\n\n    function saveHistory(entry) {\n        var key = 'vc_history_' + SLUG; var arr = [];\n        try { arr = JSON.parse(localStorage.getItem(key)) || []; } catch(e) {}\n        entry._ts = new Date().toISOString(); arr.unshift(entry);\n        if (arr.length > 10) arr = arr.slice(0, 10);\n        try { localStorage.setItem(key, JSON.stringify(arr)); } catch(e) {}\n    }\n\n    function loadParams() {\n        var p = new URLSearchParams(window.location.search);\n        p.forEach(function(v, k) { var el = $(k) || $('vc-' + k); if (el) el.value = v; });\n    }\n\n    function renderFormulas() {\n        try {\n            katex.render('F_{unbal} = \\\\frac{U}{10^6} \\\\times \\\\omega^2 \\\\quad [N]', $('vc-katex-1'), { displayMode: true, throwOnError: false });\n            katex.render('\\\\omega_n = \\\\sqrt{\\\\frac{k}{m_{total}}}, \\\\quad f_n = \\\\frac{\\\\omega_n}{2\\\\pi} \\\\quad [Hz]', $('vc-katex-2'), { displayMode: true, throwOnError: false });\n            katex.render('T = \\\\frac{\\\\sqrt{1 + (2\\\\zeta r)^2}}{\\\\sqrt{(1 - r^2)^2 + (2\\\\zeta r)^2}}, \\\\quad r = \\\\frac{\\\\omega}{\\\\omega_n}', $('vc-katex-3'), { displayMode: true, throwOnError: false });\n            katex.render('\\\\eta = (1 - T) \\\\times 100\\\\% \\\\quad \\\\text{(when } T < 1\\\\text{)}', $('vc-katex-4'), { displayMode: true, throwOnError: false });\n        } catch(e) {}\n    }\n\n    function init() { loadParams(); renderFormulas(); calculate(); }\n    if (document.readyState === 'loading') { document.addEventListener('DOMContentLoaded', init); } else { init(); }\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Kikokotoo bure cha mtandaoni kwa mtetemo wa msingi unaotokana na kukosekana usawa wa mashine. Huhesabu nguvu inayopitishwa, uwiano wa upitishaji, masafa asilia, uwiano wa masafa, na ufanisi wa kutengwa kwa mashine zilizowekwa.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100106","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100106","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100106\/revisions"}],"predecessor-version":[{"id":102115,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/calculator\/100106\/revisions\/102115"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/media?parent=100106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/categories?post=100106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/sw\/wp-json\/wp\/v2\/tags?post=100106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}