{"id":100298,"date":"2026-02-15T20:32:31","date_gmt":"2026-02-15T20:32:31","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100298"},"modified":"2026-07-17T09:05:11","modified_gmt":"2026-07-17T09:05:11","slug":"vibration-transmissibility","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/vi\/calculators\/vibration-transmissibility\/","title":{"rendered":"C\u00f4ng c\u1ee5 t\u00ednh to\u00e1n \u0111\u1ed9 truy\u1ec1n rung \u0111\u1ed9ng | C\u00f4ng c\u1ee5 tr\u1ef1c tuy\u1ebfn mi\u1ec5n ph\u00ed"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Vibration Transmissibility Calculator\",\"alternateName\":[\"Isolation Efficiency Calculator\",\"Transfer Function Calculator\",\"Transmissibility Ratio Calculator\"],\"description\":\"Free online engineering calculator for vibration transmissibility (transfer function) and isolation efficiency. Supports damped and undamped SDOF systems.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/vibration-transmissibility\/\",\"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\":[\"Transmissibility ratio T\",\"Isolation efficiency percentage\",\"Frequency ratio calculation\",\"Phase angle output\",\"Auto-calculation on input change\",\"Multiple presets\"],\"keywords\":\"vibration transmissibility, isolation efficiency, damping ratio, natural frequency, frequency ratio\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is vibration transmissibility?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Vibration transmissibility T is the ratio of the response amplitude to the excitation amplitude in a vibration isolation system. T < 1 means vibration is being isolated; T > 1 means amplification is occurring, especially near resonance.\"}},\n{\"@type\":\"Question\",\"name\":\"When does vibration isolation begin?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"For an undamped system, isolation begins when the frequency ratio r = f\/fn exceeds \u221a2 \u2248 1.414. Below this ratio, the mount amplifies vibration. The T = 1 crossover at r = \u221a2 holds for any damping ratio.\"}},\n{\"@type\":\"Question\",\"name\":\"What is a good damping ratio for isolation?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Low damping (\u03b6 = 0.01\u20130.1) gives better isolation at high frequency ratios but higher resonance peaks. Moderate damping (\u03b6 = 0.1\u20130.3) limits resonance amplification at the expense of some high-frequency isolation.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I calculate isolation efficiency?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Isolation efficiency = (1 \u2212 T) \u00d7 100%. For example, T = 0.1 means 90% isolation. This metric is only meaningful when T < 1 (frequency ratio > \u221a2).\"}},\n{\"@type\":\"Question\",\"name\":\"What is the frequency ratio r?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The frequency ratio r = f\/fn, where f is the forcing (excitation) frequency and fn is the natural frequency of the isolation system. 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font-size:13px; color:var(--vc-ink-muted); }\n.vc-footer a { color:var(--vc-accent); text-decoration:none; }\n.vc-footer a:hover { text-decoration:underline; }\n.vc-footer-links { margin-top:8px; font-size:12px; }\n.vc-footer-links a { margin:0 8px; }\n\n\/* \u2500\u2500 PRINT \u2500\u2500 *\/\n@media print {\n    .vc-section-body { max-height:none!important; }\n    .vc-faq-a { max-height:none!important; }\n    .vc-results { max-height:none!important; padding:24px!important; }\n    .vc-copy-btn, .vc-section-chevron, .vc-faq-chevron, .vc-presets, .vc-promo { display:none!important; }\n}\n.vc-results.vc-visible{max-height:5000px}\n.vc-viz{margin:20px 0;background:var(--vc-surface);border:1px solid var(--vc-border-light);border-radius:var(--vc-radius);padding:16px;overflow:hidden}\n.vc-viz svg{width:100%;height:auto;display:block}\n.vc-viz-title{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:0.1em;text-transform:uppercase;color:var(--vc-ink-muted);margin-bottom:12px}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-vibration-transmissibility\">\n\n<!-- Header -->\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool \u2014 #013<\/p>\n    <h1 class=\"vc-header-title\">Vibration Transmissibility Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate the transfer function T of a vibration isolation system. Enter forcing frequency, natural frequency, and damping ratio to get transmissibility and isolation efficiency.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">SDOF System<\/span>\n        <span class=\"vc-badge\">Transmissibility T<\/span>\n        <span class=\"vc-badge\">Isolation %<\/span>\n    <\/div>\n<\/header>\n\n<!-- Calculator Card -->\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-fforce\">Forcing Frequency <span class=\"vc-label-hint\">(Hz)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-fforce\" inputmode=\"decimal\" step=\"any\" min=\"0.01\" placeholder=\"e.g. 50\" value=\"50\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-fnat\">Natural Frequency <span class=\"vc-label-hint\">(Hz)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-fnat\" inputmode=\"decimal\" step=\"any\" min=\"0.01\" placeholder=\"e.g. 15\" value=\"15\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-zeta\">Damping Ratio \u03b6 <span class=\"vc-label-hint\">(0\u20131)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-zeta\" inputmode=\"decimal\" step=\"any\" min=\"0\" max=\"2\" placeholder=\"e.g. 0.05\" value=\"0.05\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-input-type\">Input Type<\/label>\n                <select class=\"vc-select\" id=\"vc-input-type\">\n                    <option value=\"force\" selected>Force transmissibility<\/option>\n                    <option value=\"displacement\">Displacement transmissibility<\/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-ff=\"50\" data-fn=\"10\" data-z=\"0.05\">Rubber mount \u2014 50 Hz \/ 10 Hz<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-ff=\"30\" data-fn=\"5\" data-z=\"0.1\">Spring isolator \u2014 30 Hz \/ 5 Hz<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-ff=\"120\" data-fn=\"25\" data-z=\"0.02\">Machine on pads \u2014 120 Hz \/ 25 Hz<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-ff=\"15\" data-fn=\"12\" data-z=\"0.3\">Near resonance \u2014 15 Hz \/ 12 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\">Transmissibility T<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-T\">\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 class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Frequency Ratio r<\/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\">Transmissibility (dB)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-db\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Phase Angle<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-phase\">\u2014<\/div>\n            <\/div>\n        <\/div>\n        <div class=\"vc-viz\" id=\"vc-trans-viz\"><\/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 of a SDOF System<\/h3>\n            <p>For a single-degree-of-freedom (SDOF) system with viscous damping, the transmissibility ratio T is:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <p>Where <strong>r = f \/ f<sub>n<\/sub><\/strong> is the frequency ratio and <strong>\u03b6<\/strong> is the damping ratio.<\/p>\n\n            <h3>Key Regions<\/h3>\n            <ul>\n                <li><strong>r &lt; 1<\/strong> \u2014 Below resonance: T \u2248 1 (no isolation)<\/li>\n                <li><strong>r \u2248 1<\/strong> \u2014 Resonance: T peaks (amplification)<\/li>\n                <li><strong>r = \u221a2 \u2248 1.414<\/strong> \u2014 Crossover point: T = 1 regardless of damping<\/li>\n                <li><strong>r &gt; \u221a2<\/strong> \u2014 Isolation region: T &lt; 1, vibration is reduced<\/li>\n            <\/ul>\n\n            <h3>Isolation Efficiency<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <p>Isolation efficiency is only meaningful when T &lt; 1 (i.e., r &gt; \u221a2).<\/p>\n\n            <h3>Phase Angle<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n\n            <h3>Practical Example<\/h3>\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 Machine on Rubber Mounts<\/div>\n                <p><strong>Given:<\/strong> Forcing frequency = 50 Hz, Natural frequency = 15 Hz, \u03b6 = 0.05<\/p>\n                <p>r = 50 \/ 15 = 3.333<\/p>\n                <p>T = \u221a(1 + (2 \u00d7 0.05 \u00d7 3.333)\u00b2) \/ \u221a((1 \u2212 3.333\u00b2)\u00b2 + (2 \u00d7 0.05 \u00d7 3.333)\u00b2)<\/p>\n                <p>T = \u221a(1.111) \/ \u221a(102.23 + 0.111) = 1.054 \/ 10.117 = <strong>0.104<\/strong><\/p>\n                <p>Isolation efficiency = (1 \u2212 0.104) \u00d7 100 = <strong>89.6%<\/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 formula applies to SDOF systems. Real structures may have multiple resonances. Always verify with measurements.<\/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\/vibration-overall-level\/\">Overall Vibration Level<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/vibration-velocity\/\">Vibration Velocity (ISO 10816)<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/vibration-phase-angle\/\">Phase Angle Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/campbell-diagram-calculator\/\">Campbell Diagram<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/residual-unbalance-iso1940\/\">Residual Unbalance (ISO 21940)<\/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 vibration analyzers. Measure transmissibility and isolation effectiveness 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 transmissibility and isolation efficiency. 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-transmissibility';\n\n    function $(id) { return document.getElementById(id); }\n    function fmt(n, d) { if(isNaN(n)||!isFinite(n)) return '\u2014'; var f=n.toFixed(d===undefined?4:d); return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,''); }\n\n    \/* \u2500\u2500 CALCULATION \u2500\u2500 *\/\n    function calculate() {\n        var ff = parseFloat($('vc-fforce').value);\n        var fn = parseFloat($('vc-fnat').value);\n        var zeta = parseFloat($('vc-zeta').value);\n\n        if (!ff || ff <= 0 || !fn || fn <= 0 || isNaN(zeta) || zeta < 0) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n\n        var r = ff \/ fn;\n        var r2 = r * r;\n        var zr2 = (2 * zeta * r);\n        var num = Math.sqrt(1 + zr2 * zr2);\n        var den = Math.sqrt(Math.pow(1 - r2, 2) + zr2 * zr2);\n        var T = num \/ den;\n\n        var effPct = T < 1 ? (1 - T) * 100 : 0;\n        var TdB = 20 * Math.log10(T);\n        var phaseRad = Math.atan2(2 * zeta * r * r2, (1 - r2) * (1 + (2 * zeta * r) * (2 * zeta * r) \/ (1 - r2 + 0.0001)));\n        \/\/ Simpler phase calc\n        var phi = Math.atan2(2 * zeta * r, 1 - r2) - Math.atan(2 * zeta * r);\n        if (phi < 0) phi = 0;\n        var phiDeg = phi * 180 \/ Math.PI;\n\n        $('vc-r-T').innerHTML = fmt(T, 4);\n        if (T < 1) {\n            $('vc-r-eff').innerHTML = fmt(effPct, 1) + ' <span class=\"vc-rcard-unit\">%<\/span>';\n        } else {\n            $('vc-r-eff').innerHTML = '<span style=\"color:var(--vc-red)\">Amplification \u00d7' + fmt(T, 2) + '<\/span>';\n        }\n        $('vc-r-ratio').innerHTML = fmt(r, 3);\n        $('vc-r-db').innerHTML = fmt(TdB, 1) + ' <span class=\"vc-rcard-unit\">dB<\/span>';\n        $('vc-r-phase').innerHTML = fmt(phiDeg, 1) + ' <span class=\"vc-rcard-unit\">\u00b0<\/span>';\n\n        $('vc-results').classList.add('vc-visible');\n\n      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x=\"'+(ml+pw+3)+'\" y=\"'+(ty(1)+3)+'\" fill=\"var(--vc-ink-muted)\" font-size=\"8\">T=1<\/text>';\n        s+='<line x1=\"'+rx(sq2)+'\" y1=\"'+mt+'\" x2=\"'+rx(sq2)+'\" y2=\"'+(mt+ph)+'\" stroke=\"var(--vc-ink-muted)\" stroke-width=\"0.8\" stroke-dasharray=\"3,3\"\/>';\n        s+='<text x=\"'+rx(sq2)+'\" y=\"'+(mt-5)+'\" text-anchor=\"middle\" fill=\"var(--vc-ink-muted)\" font-size=\"8\">r=\\u221A2<\/text>';\n        s+='<text x=\"'+((rx(sq2)+rx(rMax))\/2)+'\" y=\"'+ty(0.5)+'\" text-anchor=\"middle\" fill=\"var(--vc-green)\" font-size=\"9\" opacity=\"0.7\">Isolation zone<\/text>';\n        s+='<text x=\"'+((rx(0)+rx(sq2))\/2)+'\" y=\"'+ty(3)+'\" text-anchor=\"middle\" fill=\"var(--vc-red)\" font-size=\"9\" opacity=\"0.6\">Amplification<\/text>';\n        var pts='',inside=false;\n        for(var i=0;i<=200;i++){\n            var r=i\/200*rMax,zr=2*zeta*r;\n            var T=Math.sqrt(1+zr*zr)\/Math.sqrt(Math.pow(1-r*r,2)+zr*zr);\n            if(T<=tMax){pts+=(inside?'L':'M')+rx(r).toFixed(1)+','+ty(T).toFixed(1)+' ';inside=true;}\n            else{inside=false;}\n        }\n        s+='<path d=\"'+pts+'\" fill=\"none\" stroke=\"var(--vc-accent)\" stroke-width=\"2.5\"\/>';\n        if(T_op<=tMax&&r_op<=rMax){\n            s+='<circle cx=\"'+rx(r_op).toFixed(1)+'\" cy=\"'+ty(T_op).toFixed(1)+'\" r=\"5\" fill=\"var(--vc-accent)\" stroke=\"var(--vc-surface)\" stroke-width=\"2\"\/>';\n            var ly=ty(T_op)>mt+ph\/2?ty(T_op)-14:ty(T_op)+16;\n            s+='<text x=\"'+rx(r_op).toFixed(1)+'\" y=\"'+ly+'\" text-anchor=\"middle\" fill=\"var(--vc-accent)\" font-size=\"9.5\" font-weight=\"600\">T='+fmt(T_op,3)+' (r='+fmt(r_op,2)+')<\/text>';\n        }\n        if(zeta>0){var Tres=Math.sqrt(1+4*zeta*zeta)\/Math.sqrt(4*zeta*zeta);\n            if(Tres<=tMax){s+='<line x1=\"'+rx(1)+'\" y1=\"'+ty(Tres)+'\" x2=\"'+rx(1)+'\" y2=\"'+(ty(Tres)-10)+'\" stroke=\"var(--vc-red)\" stroke-width=\"1\"\/>';\n            s+='<text x=\"'+rx(1)+'\" y=\"'+(ty(Tres)-14)+'\" text-anchor=\"middle\" fill=\"var(--vc-red)\" font-size=\"8\">T(r=1)='+fmt(Tres,2)+'<\/text>';}}\n        s+='<line x1=\"'+ml+'\" y1=\"'+mt+'\" x2=\"'+ml+'\" y2=\"'+(mt+ph)+'\" stroke=\"var(--vc-ink)\" stroke-width=\"1.5\"\/>';\n        s+='<line x1=\"'+ml+'\" y1=\"'+(mt+ph)+'\" x2=\"'+(ml+pw)+'\" y2=\"'+(mt+ph)+'\" stroke=\"var(--vc-ink)\" stroke-width=\"1.5\"\/>';\n        s+='<text x=\"'+(ml+pw\/2)+'\" y=\"'+(SH-6)+'\" text-anchor=\"middle\" fill=\"var(--vc-ink-secondary)\" font-size=\"10.5\">Frequency Ratio r = f \/ f\\u2099<\/text>';\n        s+='<text x=\"14\" y=\"'+(mt+ph\/2)+'\" text-anchor=\"middle\" fill=\"var(--vc-ink-secondary)\" font-size=\"10.5\" transform=\"rotate(-90,14,'+(mt+ph\/2)+')\">Transmissibility T<\/text>';\n        s+='<\/svg>';\n        el.innerHTML='<div class=\"vc-viz-title\">Transmissibility Curve<\/div>'+s;\n    }\n\n    \/* \u2500\u2500 PRESETS \u2500\u2500 *\/\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn) {\n        btn.addEventListener('click', function(e) {\n            e.preventDefault();\n            $('vc-fforce').value = this.getAttribute('data-ff');\n            $('vc-fnat').value = this.getAttribute('data-fn');\n            $('vc-zeta').value = this.getAttribute('data-z');\n            calculate();\n        });\n    });\n\n    \/* \u2500\u2500 AUTO-CALCULATE \u2500\u2500 *\/\n    $('vc-form').addEventListener('input', calculate);\n    $('vc-form').addEventListener('change', calculate);\n\n    \/* \u2500\u2500 COPY \u2500\u2500 *\/\n    $('vc-copy-btn').addEventListener('click', function() {\n        var text = 'Vibration Transmissibility 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            'Forcing Freq: ' + $('vc-fforce').value + ' Hz\\n' +\n            'Natural Freq: ' + $('vc-fnat').value + ' Hz\\n' +\n            'Damping Ratio: ' + $('vc-zeta').value + '\\n' +\n            'Transmissibility T: ' + $('vc-r-T').textContent + '\\n' +\n            'Isolation Efficiency: ' + $('vc-r-eff').textContent + '\\n' +\n            'Frequency Ratio: ' + $('vc-r-ratio').textContent + '\\n' +\n            'T in dB: ' + $('vc-r-db').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\/vibration-transmissibility\/';\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    \/* \u2500\u2500 COLLAPSIBLE SECTIONS \u2500\u2500 *\/\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    \/* \u2500\u2500 FAQ \u2500\u2500 *\/\n    var faqData = [\n        { q:'What is vibration transmissibility?', a:'<p>Vibration transmissibility T is the ratio of the response amplitude to the excitation amplitude in a vibration isolation system. T &lt; 1 means vibration is being isolated; T &gt; 1 means amplification is occurring, especially near resonance.<\/p>' },\n        { q:'When does vibration isolation begin?', a:'<p>For an undamped system, isolation begins when the frequency ratio r = f\/f<sub>n<\/sub> exceeds \u221a2 \u2248 1.414. Below this ratio, the mount amplifies vibration rather than reducing it. The T = 1 crossover at r = \u221a2 holds for any damping ratio.<\/p>' },\n        { q:'What is a good damping ratio for vibration isolation?', a:'<p>Low damping (\u03b6 = 0.01\u20130.1) gives better isolation at high frequency ratios but results in higher resonance peaks. Moderate damping (\u03b6 = 0.1\u20130.3) limits resonance amplification at the expense of some high-frequency isolation performance.<\/p>' },\n        { q:'How do I calculate isolation efficiency?', a:'<p>Isolation efficiency = (1 \u2212 T) \u00d7 100%. For example, T = 0.1 means 90% isolation efficiency. This metric is only meaningful when T &lt; 1, i.e., when the frequency ratio r &gt; \u221a2.<\/p>' },\n        { q:'What is the frequency ratio r?', a:'<p>The frequency ratio r = f\/f<sub>n<\/sub>, where f is the forcing (excitation) frequency and f<sub>n<\/sub> is the natural frequency of the isolation system. The system\\'s dynamic response depends primarily on this ratio and the damping ratio \u03b6.<\/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    \/* \u2500\u2500 HISTORY \u2500\u2500 *\/\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)); } catch(e) {}\n    }\n\n    \/* \u2500\u2500 URL PARAMS \u2500\u2500 *\/\n    function loadParams() {\n        var p = new URLSearchParams(window.location.search);\n        if(p.get('ff')) $('vc-fforce').value = p.get('ff');\n        if(p.get('fn')) $('vc-fnat').value = p.get('fn');\n        if(p.get('z')) $('vc-zeta').value = p.get('z');\n    }\n\n    \/* \u2500\u2500 KATEX \u2500\u2500 *\/\n    function renderFormulas() {\n        try {\n            katex.render('T = \\\\frac{\\\\sqrt{1 + (2\\\\zeta r)^2}}{\\\\sqrt{(1 - r^2)^2 + (2\\\\zeta r)^2}}', $('vc-katex-1'), { displayMode:true, throwOnError:false });\n            katex.render('\\\\eta = (1 - T) \\\\times 100\\\\%', $('vc-katex-2'), { displayMode:true, throwOnError:false });\n            katex.render('\\\\phi = \\\\arctan\\\\!\\\\left(\\\\frac{2\\\\zeta r}{1 - r^2}\\\\right) - \\\\arctan(2\\\\zeta r)', $('vc-katex-3'), { displayMode:true, throwOnError:false });\n        } catch(e) {}\n    }\n\n    \/* \u2500\u2500 INIT \u2500\u2500 *\/\n    function init() {\n        loadParams();\n        renderFormulas();\n        calculate();\n    }\n    if (document.readyState === 'loading') { document.addEventListener('DOMContentLoaded', init); } else { init(); }\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>C\u00f4ng c\u1ee5 t\u00ednh to\u00e1n tr\u1ef1c tuy\u1ebfn mi\u1ec5n ph\u00ed v\u1ec1 h\u1ec7 s\u1ed1 truy\u1ec1n rung v\u00e0 hi\u1ec7u qu\u1ea3 c\u00e1ch ly. Nh\u1eadp t\u1ea7n s\u1ed1 k\u00edch th\u00edch, t\u1ea7n s\u1ed1 t\u1ef1 nhi\u00ean v\u00e0 h\u1ec7 s\u1ed1 gi\u1ea3m ch\u1ea5n \u0111\u1ec3 t\u00ednh to\u00e1n h\u1ec7 s\u1ed1 truy\u1ec1n rung T v\u00e0 ph\u1ea7n tr\u0103m c\u00e1ch ly.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100298","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100298","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":4,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100298\/revisions"}],"predecessor-version":[{"id":102647,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/calculator\/100298\/revisions\/102647"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/media?parent=100298"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/categories?post=100298"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/vi\/wp-json\/wp\/v2\/tags?post=100298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}