{"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":"2026-03-05T15:34:33","modified_gmt":"2026-03-05T15:34:33","slug":"vibration-transmissibility","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/bn\/calculators\/vibration-transmissibility\/","title":{"rendered":"\u0995\u09ae\u09cd\u09aa\u09a8 \u099f\u09cd\u09b0\u09be\u09a8\u09cd\u09b8\u09ae\u09bf\u09b8\u09bf\u09ac\u09bf\u09b2\u09bf\u099f\u09bf \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 \u099f\u09c1\u09b2"},"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. With damping, the crossover point shifts slightly.\"}},\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. The system response depends primarily on this ratio and the damping ratio \u03b6.\"}}\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\":\"Vibration Transmissibility Calculator\",\"item\":\"https:\/\/vibromera.eu\/calculators\/vibration-transmissibility\/\"}\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 href=\"https:\/\/fonts.googleapis.com\/css2?family=DM+Sans:ital,opsz,wght@0,9..40,300;0,9..40,400;0,9..40,500;0,9..40,600;0,9..40,700;1,9..40,400&#038;family=JetBrains+Mono:wght@400;500;600&#038;family=Fraunces:opsz,wght@9..144,700;9..144,800&#038;display=swap\" rel=\"stylesheet\">\n\n<link rel=\"stylesheet\" href=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.css\">\n\n<style>\n:root {\n    --vc-bg: #f4f1ec;\n    --vc-surface: #ffffff;\n    --vc-surface-alt: #f8f6f2;\n    --vc-ink: #1a1a1a;\n    --vc-ink-secondary: #5a5650;\n    --vc-ink-muted: #8a857e;\n    --vc-accent: #c85a2a;\n    --vc-accent-hover: #b04d22;\n    --vc-accent-light: #fdf0ea;\n    --vc-blue: #2a5c8c;\n    --vc-blue-light: #eaf1f8;\n    --vc-green: #2a7a4b;\n    --vc-green-light: #eaf8ef;\n    --vc-yellow: #a67c00;\n    --vc-yellow-light: #fef9e8;\n    --vc-red: #b91c1c;\n    --vc-red-light: #fef2f2;\n    --vc-border: #d9d4cc;\n    --vc-border-light: #e8e4dd;\n    --vc-shadow: 0 1px 3px rgba(26,26,26,0.06), 0 4px 12px rgba(26,26,26,0.04);\n    --vc-shadow-lg: 0 4px 12px rgba(26,26,26,0.08), 0 16px 40px rgba(26,26,26,0.06);\n    --vc-radius: 8px;\n    --vc-radius-lg: 12px;\n    --vc-font: 'DM Sans', -apple-system, BlinkMacSystemFont, 'Segoe UI', sans-serif;\n    --vc-mono: 'JetBrains Mono', 'Consolas', 'Monaco', monospace;\n    --vc-display: 'Fraunces', Georgia, serif;\n}\n\n.vc-calculator {\n    font-family: var(--vc-font);\n    font-size: 15px;\n    line-height: 1.65;\n    color: var(--vc-ink);\n    max-width: 960px;\n    margin: 0 auto;\n    padding: 20px 16px 40px;\n    -webkit-font-smoothing: antialiased;\n}\n.vc-calculator *, .vc-calculator *::before, .vc-calculator *::after { box-sizing: border-box; }\n\n\/* \u2500\u2500 HEADER \u2500\u2500 *\/\n.vc-header { text-align: center; padding: 48px 24px 40px; position: relative; }\n.vc-header::after { content:''; position:absolute; bottom:0; left:50%; transform:translateX(-50%); width:80px; height:3px; background:var(--vc-accent); border-radius:2px; }\n.vc-header-eyebrow { font-family:var(--vc-mono); font-size:11px; font-weight:500; letter-spacing:0.15em; text-transform:uppercase; color:var(--vc-accent); margin:0 0 12px; }\n.vc-header-title { font-family:var(--vc-display); font-size:clamp(24px,4vw,36px); font-weight:800; line-height:1.15; color:var(--vc-ink); margin:0 0 16px; letter-spacing:-0.02em; }\n.vc-header-subtitle { font-size:15px; color:var(--vc-ink-secondary); margin:0 auto 20px; max-width:600px; }\n.vc-badges { display:inline-flex; gap:8px; flex-wrap:wrap; justify-content:center; }\n.vc-badge { font-family:var(--vc-mono); font-size:11px; font-weight:500; padding:4px 10px; border-radius:4px; background:var(--vc-surface); border:1px solid var(--vc-border); color:var(--vc-ink-secondary); }\n\n\/* \u2500\u2500 CARD \u2500\u2500 *\/\n.vc-card { background:var(--vc-surface); border:1px solid var(--vc-border); border-radius:var(--vc-radius-lg); box-shadow:var(--vc-shadow); overflow:hidden; margin-top:32px; }\n\n\/* \u2500\u2500 FORM \u2500\u2500 *\/\n.vc-form { padding:24px; }\n.vc-form-grid { display:grid; grid-template-columns:1fr 1fr; gap:18px; }\n@media(max-width:600px) { .vc-form-grid { grid-template-columns:1fr; } }\n.vc-field { display:flex; flex-direction:column; }\n.vc-field-full { grid-column: 1 \/ -1; }\n.vc-label { font-size:12px; font-weight:600; letter-spacing:0.04em; text-transform:uppercase; color:var(--vc-ink-secondary); margin-bottom:6px; }\n.vc-label-hint { font-weight:400; text-transform:none; letter-spacing:0; color:var(--vc-ink-muted); font-size:11px; }\n.vc-select, .vc-input { width:100%; padding:10px 12px; border:1.5px solid var(--vc-border); border-radius:6px; font-family:var(--vc-font); font-size:14px; color:var(--vc-ink); background:var(--vc-surface); transition:border-color 0.15s, box-shadow 0.15s; }\n.vc-select { padding-right:36px; appearance:none; -webkit-appearance:none; cursor:pointer; background-image:url(\"data:image\/svg+xml,%3Csvg xmlns='http:\/\/www.w3.org\/2000\/svg' width='16' height='16' fill='none' stroke='%235a5650' stroke-width='2'%3E%3Cpath d='M4 6l4 4 4-4'\/%3E%3C\/svg%3E\"); background-repeat:no-repeat; background-position:right 10px center; }\n.vc-select:focus, .vc-input:focus { outline:none; border-color:var(--vc-accent); box-shadow:0 0 0 3px rgba(200,90,42,0.12); }\n.vc-select:hover, .vc-input:hover { border-color:var(--vc-ink-muted); }\n\n\/* \u2500\u2500 PRESETS \u2500\u2500 *\/\n.vc-presets { display:flex; flex-wrap:wrap; gap:8px; margin-top:18px; padding-top:18px; border-top:1px solid var(--vc-border-light); }\n.vc-presets-label { font-family:var(--vc-mono); font-size:11px; font-weight:500; letter-spacing:0.1em; text-transform:uppercase; color:var(--vc-ink-muted); width:100%; margin-bottom:2px; }\n.vc-preset-btn { padding:5px 12px; font-family:var(--vc-font); font-size:12px; font-weight:500; border:1px solid var(--vc-border); border-radius:6px; background:var(--vc-surface-alt); color:var(--vc-ink-secondary); cursor:pointer; transition:all 0.15s; }\n.vc-preset-btn:hover { border-color:var(--vc-accent); color:var(--vc-accent); background:var(--vc-accent-light); }\n\n\/* \u2500\u2500 RESULTS \u2500\u2500 *\/\n.vc-results { border-top:1px solid var(--vc-border-light); background:var(--vc-surface-alt); padding:0; max-height:0; overflow:hidden; transition:max-height 0.5s cubic-bezier(0.4,0,0.2,1), padding 0.3s; }\n.vc-results.vc-visible { max-height:2000px; padding:24px; }\n.vc-results-head { display:flex; align-items:center; justify-content:space-between; margin-bottom:18px; }\n.vc-results-title { font-family:var(--vc-display); font-size:20px; font-weight:700; color:var(--vc-ink); margin:0; }\n.vc-copy-btn { display:inline-flex; align-items:center; gap:5px; padding:6px 12px; border:1px solid var(--vc-border); border-radius:6px; background:var(--vc-surface); font-family:var(--vc-font); font-size:12px; font-weight:500; color:var(--vc-ink-secondary); cursor:pointer; transition:all 0.15s; }\n.vc-copy-btn:hover { border-color:var(--vc-accent); color:var(--vc-accent); }\n.vc-copy-btn.vc-copied { background:var(--vc-green-light); border-color:var(--vc-green); color:var(--vc-green); }\n\n.vc-result-grid { display:grid; grid-template-columns:1fr 1fr; gap:12px; margin-bottom:20px; }\n@media(max-width:500px) { .vc-result-grid { grid-template-columns:1fr; } }\n.vc-rcard { background:var(--vc-surface); border:1px solid var(--vc-border-light); border-radius:var(--vc-radius); padding:16px; transition:transform 0.2s; }\n.vc-rcard:hover { transform:translateY(-1px); }\n.vc-rcard-primary { border-color:var(--vc-accent); border-width:2px; background:linear-gradient(135deg, #fdf6f2 0%, var(--vc-surface) 100%); grid-column:1 \/ -1; }\n.vc-rcard-label { font-family:var(--vc-mono); font-size:10px; font-weight:500; letter-spacing:0.1em; text-transform:uppercase; color:var(--vc-ink-muted); margin-bottom:4px; }\n.vc-rcard-value { font-family:var(--vc-mono); font-size:22px; font-weight:600; color:var(--vc-ink); line-height:1.2; }\n.vc-rcard-primary .vc-rcard-value { font-size:30px; color:var(--vc-accent); }\n.vc-rcard-unit { font-size:14px; font-weight:400; color:var(--vc-ink-secondary); }\n\n\/* \u2500\u2500 COLLAPSIBLE SECTIONS \u2500\u2500 *\/\n.vc-section { margin-top:24px; border:1px solid var(--vc-border); border-radius:var(--vc-radius-lg); background:var(--vc-surface); box-shadow:var(--vc-shadow); overflow:hidden; }\n.vc-section-toggle { width:100%; display:flex; align-items:center; justify-content:space-between; padding:18px 24px; border:none; background:transparent; cursor:pointer; font-family:var(--vc-font); text-align:left; transition:background 0.15s; }\n.vc-section-toggle:hover { background:var(--vc-surface-alt); }\n.vc-section-toggle-text { display:flex; align-items:center; gap:10px; }\n.vc-section-icon { font-size:20px; line-height:1; }\n.vc-section-title { font-family:var(--vc-display); font-size:18px; font-weight:700; color:var(--vc-ink); margin:0; }\n.vc-section-chevron { width:20px; height:20px; color:var(--vc-ink-muted); transition:transform 0.3s; flex-shrink:0; }\n.vc-section.vc-open .vc-section-chevron { transform:rotate(180deg); }\n.vc-section-body { max-height:0; overflow:hidden; transition:max-height 0.4s cubic-bezier(0.4,0,0.2,1); }\n.vc-section.vc-open .vc-section-body { max-height:20000px; }\n.vc-section-inner { padding:0 24px 24px; border-top:1px solid var(--vc-border-light); }\n\n\/* \u2500\u2500 THEORY \u2500\u2500 *\/\n.vc-theory h3 { font-family:var(--vc-display); font-size:17px; font-weight:700; color:var(--vc-ink); margin:28px 0 10px; }\n.vc-theory h3:first-child { margin-top:20px; }\n.vc-theory p { font-size:14px; color:var(--vc-ink-secondary); margin:0 0 10px; }\n.vc-theory ul, .vc-theory ol { font-size:14px; color:var(--vc-ink-secondary); margin:0 0 12px 18px; padding:0; }\n.vc-theory li { margin-bottom:5px; }\n.vc-formula-box { background:var(--vc-surface-alt); border:2px solid var(--vc-border); border-radius:6px; padding:14px 20px; font-family:var(--vc-mono); font-size:16px; font-weight:500; text-align:center; margin:14px 0; color:var(--vc-ink); overflow-x:auto; }\n.vc-info-box { background:var(--vc-blue-light); border-left:3px solid var(--vc-blue); padding:14px 16px; border-radius:0 6px 6px 0; margin:14px 0; }\n.vc-info-box p { margin:0; font-size:14px; color:var(--vc-ink-secondary); }\n.vc-warning-box { background:var(--vc-yellow-light); border-left:3px solid var(--vc-yellow); padding:14px 16px; border-radius:0 6px 6px 0; margin:14px 0; }\n.vc-example-box { background:var(--vc-surface-alt); border:1px solid var(--vc-border-light); border-radius:6px; padding:16px; margin:14px 0; }\n.vc-example-title { font-family:var(--vc-mono); font-size:13px; font-weight:600; color:var(--vc-accent); margin-bottom:8px; }\n.vc-table { width:100%; border-collapse:collapse; margin:14px 0; font-size:13px; }\n.vc-table th, .vc-table td { padding:10px 12px; border:1px solid var(--vc-border-light); text-align:left; }\n.vc-table th { background:var(--vc-surface-alt); font-size:11px; font-weight:600; text-transform:uppercase; letter-spacing:0.05em; color:var(--vc-ink-secondary); }\n.vc-table tr:nth-child(even) { background:var(--vc-surface-alt); }\n@media(max-width:600px) { .vc-table { font-size:12px; } .vc-table th, .vc-table td { padding:8px; } }\n\n\/* \u2500\u2500 FAQ \u2500\u2500 *\/\n.vc-faq-list { display:flex; flex-direction:column; gap:8px; margin-top:20px; }\n.vc-faq-item { border:1px solid var(--vc-border-light); border-radius:6px; overflow:hidden; }\n.vc-faq-q { width:100%; display:flex; align-items:center; justify-content:space-between; gap:12px; padding:14px 16px; border:none; background:var(--vc-surface-alt); cursor:pointer; font-family:var(--vc-font); font-size:15px; font-weight:600; color:var(--vc-ink); text-align:left; transition:background 0.15s; }\n.vc-faq-q:hover { background:#ede9e3; }\n.vc-faq-chevron { width:16px; height:16px; color:var(--vc-ink-muted); flex-shrink:0; transition:transform 0.25s; }\n.vc-faq-item.vc-open .vc-faq-chevron { transform:rotate(180deg); }\n.vc-faq-a { max-height:0; overflow:hidden; transition:max-height 0.35s; }\n.vc-faq-item.vc-open .vc-faq-a { max-height:1200px; }\n.vc-faq-a-inner { padding:14px 16px; border-top:1px solid var(--vc-border-light); font-size:14px; color:var(--vc-ink-secondary); }\n.vc-faq-a-inner p { margin:0 0 8px; }\n.vc-faq-a-inner p:last-child { margin-bottom:0; }\n.vc-faq-a-inner ul { margin:4px 0 8px 16px; padding:0; }\n.vc-faq-a-inner li { margin-bottom:3px; }\n\n\/* \u2500\u2500 RELATED \u2500\u2500 *\/\n.vc-related { display:flex; flex-wrap:wrap; gap:10px; margin-top:16px; }\n.vc-related-link { display:inline-block; padding:8px 16px; font-family:var(--vc-font); font-size:13px; font-weight:600; background:var(--vc-surface-alt); color:var(--vc-ink-secondary); border:1px solid var(--vc-border); border-radius:var(--vc-radius); text-decoration:none; transition:all 0.15s; }\n.vc-related-link:hover { border-color:var(--vc-accent); color:var(--vc-accent); background:var(--vc-accent-light); }\n\n\/* \u2500\u2500 PROMO \u2500\u2500 *\/\n.vc-promo { margin-top:24px; padding:20px; background:linear-gradient(135deg, var(--vc-accent-light), var(--vc-surface)); border:1px solid var(--vc-border); border-radius:var(--vc-radius-lg); display:flex; align-items:center; gap:16px; }\n.vc-promo-text { flex:1; font-size:14px; color:var(--vc-ink-secondary); }\n.vc-promo-text strong { color:var(--vc-ink); }\n.vc-promo-link { padding:8px 20px; font-size:13px; font-weight:700; color:#fff; background:var(--vc-accent); border-radius:var(--vc-radius); text-decoration:none; white-space:nowrap; transition:background 0.15s; }\n.vc-promo-link:hover { background:var(--vc-accent-hover); }\n\n\/* \u2500\u2500 FOOTER \u2500\u2500 *\/\n.vc-footer { text-align:center; padding:32px 16px; 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(112.11 + 0.111) = 1.054 \/ 10.595 = <strong>0.0995<\/strong><\/p>\n                <p>Isolation efficiency = (1 \u2212 0.0995) \u00d7 100 = <strong>90.0%<\/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);\n        if (phi < 0) phi += Math.PI;\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        $('vc-results').classList.add('vc-visible');\n\n        \/\/ URL params\n        var u = new URL(window.location);\n        u.searchParams.set('ff', ff); u.searchParams.set('fn', fn); u.searchParams.set('z', zeta);\n        history.replaceState(null, '', u.toString());\n\n        saveHistory({ ff:ff, fn:fn, zeta:zeta, T:fmt(T,4), _summary:'f='+ff+'Hz, fn='+fn+'Hz, \u03b6='+zeta });\n        drawTransViz(r, zeta, T);\n    }\n\n    function drawTransViz(r_op, zeta, T_op){\n        var el=$('vc-trans-viz');if(!el)return;\n        var SW=600,SH=350,ml=55,mr=20,mt=25,mb=50,pw=SW-ml-mr,ph=SH-mt-mb;\n        var rMax=5,tMax=5;\n        function rx(r){return ml+r\/rMax*pw;}\n        function ty(t){return mt+(1-Math.min(t,tMax)\/tMax)*ph;}\n        var s='<svg viewBox=\"0 0 600 350\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" style=\"font-family:var(--vc-mono)\">';\n        var sq2=Math.sqrt(2);\n        s+='<rect x=\"'+rx(sq2)+'\" y=\"'+ty(1)+'\" width=\"'+(rx(rMax)-rx(sq2))+'\" height=\"'+(ty(0)-ty(1))+'\" fill=\"rgba(42,122,75,0.08)\"\/>';\n        s+='<rect x=\"'+rx(0)+'\" y=\"'+ty(tMax)+'\" width=\"'+(rx(sq2)-rx(0))+'\" height=\"'+(ty(1)-ty(tMax))+'\" fill=\"rgba(185,28,28,0.05)\"\/>';\n        for(var g=0;g<=5;g++){\n            s+='<line x1=\"'+rx(g)+'\" y1=\"'+mt+'\" x2=\"'+rx(g)+'\" y2=\"'+(mt+ph)+'\" stroke=\"var(--vc-border-light)\" stroke-width=\"0.7\"\/>';\n            s+='<text x=\"'+rx(g)+'\" y=\"'+(SH-mb+16)+'\" text-anchor=\"middle\" fill=\"var(--vc-ink-muted)\" font-size=\"9\">'+g+'<\/text>';\n        }\n        for(var g=0;g<=5;g++){\n            s+='<line x1=\"'+ml+'\" y1=\"'+ty(g)+'\" x2=\"'+(ml+pw)+'\" y2=\"'+ty(g)+'\" stroke=\"var(--vc-border-light)\" stroke-width=\"0.7\"\/>';\n            s+='<text x=\"'+(ml-6)+'\" y=\"'+(ty(g)+3)+'\" text-anchor=\"end\" fill=\"var(--vc-ink-muted)\" font-size=\"9\">'+g+'<\/text>';\n        }\n        s+='<line x1=\"'+ml+'\" y1=\"'+ty(1)+'\" x2=\"'+(ml+pw)+'\" y2=\"'+ty(1)+'\" stroke=\"var(--vc-ink-muted)\" stroke-width=\"1\" stroke-dasharray=\"4,3\"\/>';\n        s+='<text 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\">Peak T='+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. With damping present, the crossover point shifts slightly.<\/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)', $('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>\u0995\u09ae\u09cd\u09aa\u09a8 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u09a8\u09cd\u09a4\u09b0\u09af\u09cb\u0997\u09cd\u09af\u09a4\u09be \u098f\u09ac\u0982 \u09ac\u09bf\u099a\u09cd\u099b\u09bf\u09a8\u09cd\u09a8\u09a4\u09be \u09a6\u0995\u09cd\u09b7\u09a4\u09be\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 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u09a8\u09cd\u09a4\u09b0 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf, \u09aa\u09cd\u09b0\u09be\u0995\u09c3\u09a4\u09bf\u0995 \u09ab\u09cd\u09b0\u09bf\u0995\u09cb\u09af\u09bc\u09c7\u09a8\u09cd\u09b8\u09bf \u098f\u09ac\u0982 \u09a1\u09cd\u09af\u09be\u09ae\u09cd\u09aa\u09bf\u0982 \u0985\u09a8\u09c1\u09aa\u09be\u09a4 \u09aa\u09cd\u09b0\u09ac\u09c7\u09b6 \u0995\u09b0\u09c1\u09a8 \u09b8\u09cd\u09a5\u09be\u09a8\u09be\u09a8\u09cd\u09a4\u09b0\u09af\u09cb\u0997\u09cd\u09af\u09a4\u09be T \u098f\u09ac\u0982 \u09ac\u09bf\u099a\u09cd\u099b\u09bf\u09a8\u09cd\u09a8\u09a4\u09be \u09b6\u09a4\u09be\u0982\u09b6 \u0997\u09a3\u09a8\u09be \u0995\u09b0\u09a4\u09c7\u0964<\/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\/bn\/wp-json\/wp\/v2\/calculator\/100298","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":2,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100298\/revisions"}],"predecessor-version":[{"id":100736,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/calculator\/100298\/revisions\/100736"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/media?parent=100298"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/categories?post=100298"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/bn\/wp-json\/wp\/v2\/tags?post=100298"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}