{"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":"2026-02-15T20:16:52","modified_gmt":"2026-02-15T20:16:52","slug":"foundation-vibration-from-machine","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/foundation-vibration-from-machine\/","title":{"rendered":"\u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u0995\u09ae\u09cd\u09aa\u09a8 \u09ae\u09c7\u09b6\u09bf\u09a8 \u09a5\u09c7\u0995\u09c7 | \u09b8\u0982\u0995\u09cd\u09b0\u09ae\u09bf\u09a4 \u09ac\u09b2"},"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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16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}\n@media print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-foundation-vibration\">\n\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool<\/p>\n    <h1 class=\"vc-header-title\">Foundation Vibration from Machine<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate the transmitted force from machine unbalance to foundation, transmissibility ratio, natural frequency, and vibration isolation efficiency.<\/p>\n    <div class=\"vc-badges\">\n        <span 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 \u2248 0.0206, F<sub>transmitted<\/sub> = 296.1 \u00d7 0.0206 = <strong>6.1 N<\/strong><\/p>\n                <p>Isolation efficiency = <strong>97.9%<\/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>\u09ae\u09c7\u09b6\u09bf\u09a8\u09c7\u09b0 \u0985\u09b8\u09a8\u09cd\u09a4\u09c1\u09b2\u09a8\u099c\u09a8\u09bf\u09a4 \u09ad\u09bf\u09a4\u09cd\u09a4\u09bf \u0995\u09ae\u09cd\u09aa\u09a8\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09ac\u09bf\u09a8\u09be\u09ae\u09c2\u09b2\u09cd\u09af\u09c7 \u0985\u09a8\u09b2\u09be\u0987\u09a8 \u0995\u09cd\u09af\u09be\u09b2\u0995\u09c1\u09b2\u09c7\u099f\u09b0\u0964 \u09aa\u09cd\u09b0\u09c7\u09b0\u09bf\u09a4 \u09ac\u09b2, \u099f\u09cd\u09b0\u09be\u09a8\u09cd\u09b8\u09ae\u09bf\u09b8\u09bf\u09ac\u09bf\u09b2\u09bf\u099f\u09bf \u0985\u09a8\u09c1\u09aa\u09be\u09a4, \u09aa\u09cd\u09b0\u09be\u0995\u09c3\u09a4\u09bf\u0995 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf, \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u098f\u09ac\u0982 \u09b8\u09cd\u09a5\u09be\u09aa\u09bf\u09a4 \u09af\u09a8\u09cd\u09a4\u09cd\u09b0\u09aa\u09be\u09a4\u09bf\u09b0 \u099c\u09a8\u09cd\u09af \u09ac\u09bf\u099a\u09cd\u099b\u09bf\u09a8\u09cd\u09a8\u0995\u09b0\u09a3 \u09a6\u0995\u09cd\u09b7\u09a4\u09be \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09c1\u09a8\u0964<\/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\/bn\/wp-json\/wp\/v2\/calculator\/100106","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":1,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100106\/revisions"}],"predecessor-version":[{"id":100407,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100106\/revisions\/100407"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}