<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e293b;
      background: transparent;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      min-height: 100vh;
      padding: 6px 10px 10px;
      user-select: none;
    }

    .diagram-container {
      width: 100%;
      max-width: 620px;
      display: flex;
      flex-direction: column;
      align-items: center;
    }

    .diagram-svg {
      width: 100%;
      height: auto;
      display: block;
    }

    /* Halo / readable text style over SVG lines */
    .halo-text {
      paint-order: stroke fill;
      stroke: #ffffff;
      stroke-width: 3.5px;
      stroke-linecap: round;
      stroke-linejoin: round;
    }

    .controls {
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: center;
      gap: 10px 14px;
      width: 100%;
      max-width: 520px;
      margin-top: 6px;
      background: #f1f5f9;
      padding: 8px 14px;
      border-radius: 16px;
    }

    .slider-wrap {
      display: flex;
      align-items: center;
      gap: 8px;
      flex: 1 1 200px;
      min-width: 170px;
    }

    .slider-label {
      font-size: 13px;
      font-weight: 700;
      color: #334155;
      display: flex;
      align-items: center;
      gap: 4px;
      white-space: nowrap;
    }

    .slider-label span {
      color: #0284c7;
      font-style: italic;
    }

    input[type="range"] {
      flex: 1;
      accent-color: #2563eb;
      cursor: pointer;
      height: 6px;
      min-width: 80px;
    }

    .eq-pill {
      font-size: 13px;
      font-weight: 700;
      color: #0f172a;
      background: #e0f2fe;
      border: 1.5px solid #38bdf8;
      border-radius: 20px;
      padding: 4px 12px;
      white-space: nowrap;
      display: inline-flex;
      align-items: center;
      gap: 5px;
      box-shadow: 0 1px 2px rgba(0,0,0,0.04);
    }

    @media (max-width: 420px) {
      body { padding: 4px 6px 8px; }
      .controls {
        padding: 6px 10px;
        gap: 6px 10px;
        border-radius: 12px;
      }
      .slider-label { font-size: 12px; }
      .eq-pill { font-size: 11px; padding: 3px 9px; }
    }
  </style>
</head>
<body>

  <div class="diagram-container">
    <svg class="diagram-svg" viewBox="0 0 620 395">
      <defs>
        
        <pattern id="hatch" width="10" height="10" patternTransform="rotate(45 0 0)" patternUnits="userSpaceOnUse">
          <line x1="0" y1="0" x2="0" y2="10" stroke="#94a3b8" stroke-width="2" />
        </pattern>

        
        <marker id="arr-blue" viewBox="0 0 8 8" refX="4" refY="4" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 8 L 4 0 L 8 8 z" fill="#2563eb" />
        </marker>
        <marker id="arr-green" viewBox="0 0 8 8" refX="4" refY="4" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 8 L 4 0 L 8 8 z" fill="#059669" />
        </marker>
        <marker id="arr-purple" viewBox="0 0 8 8" refX="4" refY="4" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 8 L 4 0 L 8 8 z" fill="#7c3aed" />
        </marker>
        <marker id="arr-weight" viewBox="0 0 8 8" refX="4" refY="4" markerWidth="6" markerHeight="6" orient="auto">
          <path d="M 0 0 L 8 0 L 4 8 z" fill="#dc2626" />
        </marker>
      </defs>

      
      <rect x="40" y="18" width="230" height="12" fill="url(#hatch)" />
      <line x1="40" y1="30" x2="270" y2="30" stroke="#475569" stroke-width="3" stroke-linecap="round" />

      <rect x="380" y="18" width="190" height="12" fill="url(#hatch)" />
      <line x1="380" y1="30" x2="570" y2="30" stroke="#475569" stroke-width="3" stroke-linecap="round" />

      
      <text x="155" y="14" text-anchor="middle" font-size="12" font-weight="800" fill="#64748b" letter-spacing="1">PARALLEL SPRINGS</text>
      <text x="475" y="14" text-anchor="middle" font-size="12" font-weight="800" fill="#64748b" letter-spacing="1">EQUIVALENT SYSTEM</text>

      
      <line x1="25" y1="120" x2="585" y2="120" stroke="#cbd5e1" stroke-width="1.5" stroke-dasharray="4 4" />
      <text x="315" y="115" text-anchor="middle" font-size="11" font-weight="600" fill="#94a3b8" class="halo-text">Rest Position (x = 0)</text>

      
      
      <path id="spring1" d="" fill="none" stroke="#2563eb" stroke-width="3.5" stroke-linecap="round" stroke-linejoin="round" />
      
      <text id="label-k1" x="52" y="80" text-anchor="middle" font-size="14" font-weight="800" fill="#2563eb" class="halo-text">k₁</text>

      
      <path id="spring2" d="" fill="none" stroke="#059669" stroke-width="4.5" stroke-linecap="round" stroke-linejoin="round" />
      
      <text id="label-k2" x="258" y="80" text-anchor="middle" font-size="14" font-weight="800" fill="#059669" class="halo-text">k₂</text>

      
      <rect id="rigidBar" x="70" y="120" width="170" height="9" rx="3" fill="#334155" />

      
      <g id="loadLeft">
        <rect x="130" y="129" width="50" height="34" rx="5" fill="#fef2f2" stroke="#dc2626" stroke-width="2" />
        <text x="155" y="151" text-anchor="middle" font-size="12" font-weight="800" fill="#dc2626">F_total</text>
      </g>

      
      
      <line id="force1" x1="78" y1="120" x2="78" y2="75" stroke="#2563eb" stroke-width="2.5" marker-end="url(#arr-blue)" />
      <text id="force1-text" x="78" y="68" text-anchor="middle" font-size="11.5" font-weight="700" fill="#2563eb" class="halo-text">F₁ = k₁x</text>

      
      <line id="force2" x1="232" y1="120" x2="232" y2="55" stroke="#059669" stroke-width="2.5" marker-end="url(#arr-green)" />
      <text id="force2-text" x="232" y="48" text-anchor="middle" font-size="11.5" font-weight="700" fill="#059669" class="halo-text">F₂ = k₂x</text>

      
      <line id="gravLeft" x1="155" y1="165" x2="155" y2="205" stroke="#dc2626" stroke-width="2.5" marker-end="url(#arr-weight)" />

      
      
      <path id="springEq" d="" fill="none" stroke="#7c3aed" stroke-width="6" stroke-linecap="round" stroke-linejoin="round" />
      
      <text id="label-keq" x="515" y="80" text-anchor="start" font-size="13" font-weight="800" fill="#7c3aed" class="halo-text">k_p = k₁ + k₂</text>

      
      <g id="loadRight">
        <rect x="450" y="125" width="50" height="34" rx="5" fill="#fef2f2" stroke="#dc2626" stroke-width="2" />
        <text x="475" y="147" text-anchor="middle" font-size="12" font-weight="800" fill="#dc2626">F_total</text>
      </g>

      
      <line id="forceEq" x1="432" y1="125" x2="432" y2="50" stroke="#7c3aed" stroke-width="3" marker-end="url(#arr-purple)" />
      <text id="forceEq-text" x="432" y="42" text-anchor="middle" font-size="11.5" font-weight="700" fill="#7c3aed" class="halo-text">F = (k₁+k₂)x</text>

      
      <line id="gravRight" x1="475" y1="161" x2="475" y2="201" stroke="#dc2626" stroke-width="2.5" marker-end="url(#arr-weight)" />

      
      <g id="stretchGroup">
        
      </g>

      
      <g id="equationBox" transform="translate(100, 318)">
        <rect x="0" y="0" width="420" height="60" rx="10" fill="#f8fafc" stroke="#cbd5e1" stroke-width="1.5" />
        <text x="210" y="24" text-anchor="middle" font-size="13.5" font-weight="600" fill="#475569">
          F_total = F₁ + F₂  →  k_p · x = k₁x + k₂x
        </text>
        <text x="210" y="48" text-anchor="middle" font-size="15.5" font-weight="800" fill="#2563eb">
          k_parallel = k₁ + k₂
        </text>
      </g>
    </svg>

    <div class="controls">
      <div class="slider-wrap">
        <label class="slider-label" for="stretchSlider">Stretch (<span>x</span>):</label>
        <input type="range" id="stretchSlider" min="15" max="95" value="50" aria-label="Stretch distance x">
      </div>
      <div class="eq-pill">
        <span>Stiffness adds in parallel</span>
      </div>
    </div>
  </div>

  <script>
    const slider = document.getElementById('stretchSlider');
    const yTop = 30;
    const yRest = 120;
    const coils = 7;

    function generateSpringPath(startX, startY, endY, width) {
      const h = endY - startY;
      let d = `M ${startX} ${startY} L ${startX} ${startY + 6}`;
      const numPoints = coils * 2 - 1;
      for (let i = 0; i < numPoints; i++) {
        const x = startX + ((i % 2 === 0) ? width : -width);
        const y = startY + 6 + (i + 0.5) * (h - 12) / numPoints;
        d += ` L ${x} ${y}`;
      }
      d += ` L ${startX} ${endY - 6} L ${startX} ${endY}`;
      return d;
    }

    function update() {
      const x = parseFloat(slider.value);
      const currentY = yRest + x;

      // Update Springs (x1=105, x2=205, eq=475)
      document.getElementById('spring1').setAttribute('d', generateSpringPath(105, yTop, currentY, 11));
      document.getElementById('spring2').setAttribute('d', generateSpringPath(205, yTop, currentY, 13));
      document.getElementById('springEq').setAttribute('d', generateSpringPath(475, yTop, currentY, 16));

      // Update Spring Labels position along spring vertical center
      const midY = (yTop + currentY) / 2 + 4;
      document.getElementById('label-k1').setAttribute('y', midY);
      document.getElementById('label-k2').setAttribute('y', midY);
      document.getElementById('label-keq').setAttribute('y', midY);

      // Update Rigid Bar & Loads
      document.getElementById('rigidBar').setAttribute('y', currentY);
      
      const loadLeft = document.getElementById('loadLeft');
      loadLeft.setAttribute('transform', `translate(0, ${x})`);
      
      const loadRight = document.getElementById('loadRight');
      loadRight.setAttribute('transform', `translate(0, ${x})`);

      // Update Force vectors (proportional to stretch)
      const f1Len = 14 + x * 0.45;
      const f2Len = 20 + x * 0.70;
      const fEqLen = f1Len + f2Len;

      // Force 1
      const f1 = document.getElementById('force1');
      f1.setAttribute('y1', currentY);
      f1.setAttribute('y2', currentY - f1Len);
      const f1T = document.getElementById('force1-text');
      f1T.setAttribute('y', currentY - f1Len - 6);

      // Force 2
      const f2 = document.getElementById('force2');
      f2.setAttribute('y1', currentY);
      f2.setAttribute('y2', currentY - f2Len);
      const f2T = document.getElementById('force2-text');
      f2T.setAttribute('y', currentY - f2Len - 6);

      // Force Eq (capped so it never shoots through ceiling)
      const maxEqLen = Math.min(fEqLen, currentY - yTop - 15);
      const fEq = document.getElementById('forceEq');
      fEq.setAttribute('y1', currentY);
      fEq.setAttribute('y2', currentY - maxEqLen);
      const fEqT = document.getElementById('forceEq-text');
      fEqT.setAttribute('y', currentY - maxEqLen - 6);

      // Gravity arrows
      const gravLeft = document.getElementById('gravLeft');
      gravLeft.setAttribute('y1', 165 + x);
      gravLeft.setAttribute('y2', 205 + x);

      const gravRight = document.getElementById('gravRight');
      gravRight.setAttribute('y1', 161 + x);
      gravRight.setAttribute('y2', 201 + x);

      // Stretch bar indicator (centered in the gap between systems)
      const stretchGroup = document.getElementById('stretchGroup');
      stretchGroup.innerHTML = `
        <line x1="315" y1="${yRest}" x2="315" y2="${currentY}" stroke="#0284c7" stroke-width="2" />
        <line x1="308" y1="${yRest}" x2="322" y2="${yRest}" stroke="#0284c7" stroke-width="2" />
        <line x1="308" y1="${currentY}" x2="322" y2="${currentY}" stroke="#0284c7" stroke-width="2" />
        <rect x="326" y="${yRest + x/2 - 11}" width="42" height="22" rx="4" fill="#e0f2fe" stroke="#38bdf8" stroke-width="1.2" />
        <text x="347" y="${yRest + x/2 + 5}" text-anchor="middle" font-size="12" font-weight="800" fill="#0284c7">stretch x</text>
      `;
    }

    slider.addEventListener('input', update);
    update();
  </script>
</body>
</html>

Hooke's Law and Spring Constant Combinations

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
    }

    .main-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      width: 100%;
      max-width: 580px;
    }

    .panel {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
    }

    .panel-title {
      font-size: 13px;
      font-weight: 700;
      color: #475569;
      margin-bottom: 4px;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .svg-container {
      width: 100%;
      height: 240px;
    }

    /* Math formula card */
    .math-card {
      width: 100%;
      max-width: 580px;
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 8px;
      padding: 8px 12px;
      margin-top: 8px;
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: space-around;
      gap: 8px;
      font-size: 14px;
    }

    .math-item {
      display: flex;
      align-items: center;
      gap: 6px;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      max-width: 580px;
      margin-top: 8px;
      background: #ffffff;
      font-size: 13px;
      font-weight: 600;
      color: #334155;
    }

    input[type=range] {
      flex: 1;
      max-width: 220px;
      accent-color: #0284c7;
      cursor: pointer;
    }

    .tag {
      font-size: 11px;
      padding: 2px 6px;
      border-radius: 4px;
      font-weight: 700;
    }
    .tag-k1 { background: #e0f2fe; color: #0369a1; }
    .tag-k2 { background: #fef3c7; color: #b45309; }
    .tag-keq { background: #ede9fe; color: #6d28d9; }
  </style>
</head>
<body>

  <div class="main-grid">
    
    <div class="panel">
      <div class="panel-title">Series Connection</div>
      <svg id="seriesSvg" class="svg-container" viewBox="0 0 200 240">
        
        <line x1="40" y1="12" x2="160" y2="12" stroke="#64748b" stroke-width="4" stroke-linecap="round"/>
        <line x1="50" y1="12" x2="45" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="75" y1="12" x2="70" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="100" y1="12" x2="95" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="125" y1="12" x2="120" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="150" y1="12" x2="145" y2="4" stroke="#94a3b8" stroke-width="2"/>

        
        <path id="spring1" stroke="#0284c7" stroke-width="3" fill="none" stroke-linejoin="round" stroke-linecap="round"/>
        <text id="labelK1" x="38" y="55" font-size="12" font-weight="700" fill="#0369a1">k₁</text>
        <line id="dim1Start" x1="130" y1="12" x2="155" y2="12" stroke="#94a3b8" stroke-dasharray="2,2"/>
        <line id="dim1End" x1="130" y1="75" x2="155" y2="75" stroke="#94a3b8" stroke-dasharray="2,2"/>
        <line id="dim1Line" x1="145" y1="14" x2="145" y2="73" stroke="#0284c7" stroke-width="1.5"/>
        <text id="labelX1" x="152" y="48" font-size="11" font-weight="600" fill="#0284c7">x₁</text>

        
        <circle id="node1" cx="85" cy="75" r="4" fill="#64748b"/>

        
        <path id="spring2" stroke="#d97706" stroke-width="3" fill="none" stroke-linejoin="round" stroke-linecap="round"/>
        <text id="labelK2" x="38" y="118" font-size="12" font-weight="700" fill="#b45309">k₂</text>
        <line id="dim2End" x1="130" y1="145" x2="155" y2="145" stroke="#94a3b8" stroke-dasharray="2,2"/>
        <line id="dim2Line" x1="145" y1="77" x2="145" y2="143" stroke="#d97706" stroke-width="1.5"/>
        <text id="labelX2" x="152" y="115" font-size="11" font-weight="600" fill="#d97706">x₂</text>

        
        <rect id="loadSeries" x="65" y="145" width="40" height="20" rx="3" fill="#334155"/>
        <text id="loadTextSeries" x="85" y="159" font-size="10" font-weight="700" fill="#ffffff" text-anchor="middle">F</text>
        <line id="arrowSeries" x1="85" y1="165" x2="85" y2="195" stroke="#e11d48" stroke-width="2.5" marker-end="url(#arrowhead)"/>

        <defs>
          <marker id="arrowhead" markerWidth="6" markerHeight="6" refX="3" refY="3" orient="auto">
            <polygon points="0 0, 6 3, 0 6" fill="#e11d48" />
          </marker>
        </defs>
      </svg>
    </div>

    
    <div class="panel">
      <div class="panel-title">Equivalent Spring</div>
      <svg id="equivSvg" class="svg-container" viewBox="0 0 200 240">
        
        <line x1="40" y1="12" x2="160" y2="12" stroke="#64748b" stroke-width="4" stroke-linecap="round"/>
        <line x1="50" y1="12" x2="45" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="75" y1="12" x2="70" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="100" y1="12" x2="95" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="125" y1="12" x2="120" y2="4" stroke="#94a3b8" stroke-width="2"/>
        <line x1="150" y1="12" x2="145" y2="4" stroke="#94a3b8" stroke-width="2"/>

        
        <path id="springEq" stroke="#7c3aed" stroke-width="3.5" fill="none" stroke-linejoin="round" stroke-linecap="round"/>
        <text id="labelKeq" x="32" y="85" font-size="12" font-weight="700" fill="#6d28d9">k_eq</text>

        
        <line id="dimEqStart" x1="130" y1="12" x2="165" y2="12" stroke="#94a3b8" stroke-dasharray="2,2"/>
        <line id="dimEqEnd" x1="130" y1="145" x2="165" y2="145" stroke="#94a3b8" stroke-dasharray="2,2"/>
        <line id="dimEqLine" x1="150" y1="14" x2="150" y2="143" stroke="#7c3aed" stroke-width="1.5"/>
        <text id="labelXtot" x="156" y="85" font-size="11" font-weight="600" fill="#7c3aed">x_tot</text>

        
        <rect id="loadEq" x="65" y="145" width="40" height="20" rx="3" fill="#334155"/>
        <text id="loadTextEq" x="85" y="159" font-size="10" font-weight="700" fill="#ffffff" text-anchor="middle">F</text>
        <line id="arrowEq" x1="85" y1="165" x2="85" y2="195" stroke="#e11d48" stroke-width="2.5" marker-end="url(#arrowhead)"/>
      </svg>
    </div>
  </div>

  
  <div class="controls">
    <span>Pull Force (F):</span>
    <input type="range" id="forceSlider" min="0" max="60" value="30">
    <span id="forceValue" style="min-width: 32px; color: #e11d48;">30 N</span>
  </div>

  
  <div class="math-card">
    <div class="math-item" id="eqSum"></div>
    <div style="color: #64748b; font-weight: bold;">⟺</div>
    <div class="math-item" id="eqReciprocal"></div>
    <div style="color: #64748b; font-weight: bold;">⟹</div>
    <div class="math-item" id="eqProduct"></div>
  </div>

  <script>
    // Helper to generate a clean spring SVG path
    function generateSpringPath(startX, startY, length, coils, width) {
      const topLead = 10;
      const botLead = 10;
      const activeLen = Math.max(length - topLead - botLead, 10);
      const dy = activeLen / (coils * 2);

      let d = `M ${startX} ${startY} v ${topLead}`;
      let curY = startY + topLead;

      for (let i = 0; i < coils; i++) {
        curY += dy;
        d += ` L ${startX + width / 2} ${curY}`;
        curY += dy;
        d += ` L ${startX - width / 2} ${curY}`;
      }
      d += ` L ${startX} ${curY + botLead/2} v ${botLead/2}`;
      return d;
    }

    const spring1 = document.getElementById('spring1');
    const spring2 = document.getElementById('spring2');
    const springEq = document.getElementById('springEq');
    const node1 = document.getElementById('node1');
    const loadSeries = document.getElementById('loadSeries');
    const loadTextSeries = document.getElementById('loadTextSeries');
    const arrowSeries = document.getElementById('arrowSeries');

    const loadEq = document.getElementById('loadEq');
    const loadTextEq = document.getElementById('loadTextEq');
    const arrowEq = document.getElementById('arrowEq');

    const dim1End = document.getElementById('dim1End');
    const dim1Line = document.getElementById('dim1Line');
    const labelX1 = document.getElementById('labelX1');

    const dim2End = document.getElementById('dim2End');
    const dim2Line = document.getElementById('dim2Line');
    const labelX2 = document.getElementById('labelX2');

    const dimEqEnd = document.getElementById('dimEqEnd');
    const dimEqLine = document.getElementById('dimEqLine');
    const labelXtot = document.getElementById('labelXtot');

    const forceSlider = document.getElementById('forceSlider');
    const forceValue = document.getElementById('forceValue');

    // Constants for visualization
    const L0_1 = 45; // resting length spring 1
    const L0_2 = 45; // resting length spring 2
    const L0_eq = 90; // resting length equivalent

    // Spring constants (compliance scale)
    const k1 = 1.0;  // stretch factor 1
    const k2 = 0.5;  // stretch factor 2 (stretchier)
    // 1/keq = 1/1.0 + 1/0.5 = 1 + 2 = 3 => keq = 1/3

    function update(f) {
      const x1 = f * 0.5;
      const x2 = f * 1.0;
      const xTot = x1 + x2;

      const len1 = L0_1 + x1;
      const len2 = L0_2 + x2;
      const lenEq = L0_eq + xTot;

      const y0 = 12;
      const y1 = y0 + len1;
      const y2 = y1 + len2;
      const yEq = y0 + lenEq;

      // Update Spring 1 & Node
      spring1.setAttribute('d', generateSpringPath(85, y0, len1, 5, 24));
      node1.setAttribute('cy', y1);

      // Update Spring 2
      spring2.setAttribute('d', generateSpringPath(85, y1, len2, 6, 24));

      // Series Load & Arrow
      loadSeries.setAttribute('y', y2);
      loadTextSeries.setAttribute('y', y2 + 14);
      arrowSeries.setAttribute('y1', y2 + 20);
      arrowSeries.setAttribute('y2', y2 + 20 + 20 + f * 0.2);

      // Series Dimension 1
      dim1End.setAttribute('y1', y1);
      dim1End.setAttribute('y2', y1);
      dim1Line.setAttribute('y2', y1 - 2);
      labelX1.setAttribute('y', y0 + len1 / 2 + 4);

      // Series Dimension 2
      dim2End.setAttribute('y1', y2);
      dim2End.setAttribute('y2', y2);
      dim2Line.setAttribute('y1', y1 + 2);
      dim2Line.setAttribute('y2', y2 - 2);
      labelX2.setAttribute('y', y1 + len2 / 2 + 4);

      // Update Equivalent Spring
      springEq.setAttribute('d', generateSpringPath(85, y0, lenEq, 11, 26));

      // Equivalent Load & Arrow
      loadEq.setAttribute('y', yEq);
      loadTextEq.setAttribute('y', yEq + 14);
      arrowEq.setAttribute('y1', yEq + 20);
      arrowEq.setAttribute('y2', yEq + 20 + 20 + f * 0.2);

      // Eq Dimension
      dimEqEnd.setAttribute('y1', yEq);
      dimEqEnd.setAttribute('y2', yEq);
      dimEqLine.setAttribute('y2', yEq - 2);
      labelXtot.setAttribute('y', y0 + lenEq / 2 + 4);

      forceValue.textContent = f + " N";
    }

    forceSlider.addEventListener('input', (e) => {
      update(parseFloat(e.target.value));
    });

    // Render KaTeX expressions
    window.addEventListener('DOMContentLoaded', () => {
      if (window.katex) {
        katex.render("x_{\\text{total}} = x_1 + x_2", document.getElementById('eqSum'), { throwOnError: false });
        katex.render("\\frac{1}{k_{\\text{eq}}} = \\frac{1}{k_1} + \\frac{1}{k_2}", document.getElementById('eqReciprocal'), { throwOnError: false });
        katex.render("k_{\\text{eq}} = \\frac{k_1 k_2}{k_1 + k_2}", document.getElementById('eqProduct'), { throwOnError: false });
      } else {
        document.getElementById('eqSum').textContent = "x_total = x₁ + x₂";
        document.getElementById('eqReciprocal').textContent = "1/k_eq = 1/k₁ + 1/k₂";
        document.getElementById('eqProduct').textContent = "k_eq = (k₁·k₂)/(k₁ + k₂)";
      }
      update(30);
    });
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      width: 100%;
      height: 100%;
      background: #ffffff;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      padding: 12px 16px;
      user-select: none;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      gap: 8px;
      z-index: 10;
      flex-wrap: wrap;
      justify-content: center;
    }

    .btn-step {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 20px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: all 0.25s ease;
    }

    .btn-step.active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
    }

    .btn-play {
      background: #f8fafc;
      border: 1px solid #cbd5e1;
      border-radius: 50%;
      width: 32px;
      height: 32px;
      display: flex;
      align-items: center;
      justify-content: center;
      cursor: pointer;
      font-size: 13px;
      color: #334155;
    }

    /* Diagram Stage */
    .stage-area {
      position: relative;
      width: 100%;
      max-width: 480px;
      height: 330px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    svg {
      width: 100%;
      height: 100%;
      overflow: visible;
    }

    /* Transition groups */
    .network-group {
      transition: opacity 0.4s ease, transform 0.4s ease;
    }

    .network-group.hidden {
      opacity: 0;
      pointer-events: none;
      transform: translateY(6px);
    }

    .spring-line {
      fill: none;
      stroke-linecap: round;
      stroke-linejoin: round;
      stroke-width: 3.5;
    }

    .sp-blue { stroke: #0284c7; }
    .sp-green { stroke: #059669; }
    .sp-purple { stroke: #7c3aed; }
    .sp-amber { stroke: #d97706; }

    .bracket {
      fill: none;
      stroke: #94a3b8;
      stroke-width: 1.5;
      stroke-dasharray: 4 3;
    }

    .tag-bubble {
      font-size: 13px;
      font-weight: 700;
      paint-order: stroke;
      stroke: #ffffff;
      stroke-width: 4px;
      stroke-linejoin: round;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .tag-blue { fill: #0284c7; }
    .tag-green { fill: #059669; }
    .tag-purple { fill: #7c3aed; }
    .tag-amber { fill: #d97706; }

    .formula-tag {
      font-size: 12px;
      font-weight: 600;
      fill: #64748b;
      text-anchor: middle;
      dominant-baseline: central;
    }

    .fixture {
      fill: #475569;
      stroke: #334155;
      stroke-width: 1.5;
    }

    .load-mass {
      fill: #e2e8f0;
      stroke: #64748b;
      stroke-width: 2;
      rx: 4;
    }
  </style>
</head>
<body>

  
  <div class="controls">
    <button class="btn-play" id="playBtn" title="Play/Pause">⏸</button>
    <button class="btn-step active" data-step="0">1: Hybrid Network</button>
    <button class="btn-step" data-step="1">2: Combine Parallel</button>
    <button class="btn-step" data-step="2">3: Combine Series</button>
  </div>

  
  <div class="stage-area">
    <svg viewBox="0 0 400 320">
      <defs>
        
        <pattern id="hatch" width="8" height="8" patternTransform="rotate(45 0 0)" patternUnits="userSpaceOnUse">
          <line x1="0" y1="0" x2="0" y2="8" stroke="#cbd5e1" stroke-width="2" />
        </pattern>
      </defs>

      
      <rect x="120" y="10" width="160" height="10" fill="url(#hatch)" />
      <line x1="120" y1="20" x2="280" y2="20" stroke="#475569" stroke-width="2.5" />

      
      <g id="stage1" class="network-group">
        
        <path d="M 125 30 L 115 30 L 115 130 L 125 130" class="bracket" />
        <path d="M 275 30 L 285 30 L 285 130 L 275 130" class="bracket" />
        <text x="325" y="80" class="formula-tag">Parallel<tspan x="325" dy="16" font-weight="700" fill="#0284c7">k = k₁ + k₂</tspan></text>

        
        <line x1="160" y1="20" x2="160" y2="35" stroke="#475569" stroke-width="2" />
        <path class="spring-line sp-blue" d="M 160 35 L 150 42 L 170 54 L 150 66 L 170 78 L 150 90 L 170 102 L 150 114 L 160 120" />
        <line x1="160" y1="120" x2="160" y2="135" stroke="#475569" stroke-width="2" />
        <text x="160" y="78" class="tag-bubble tag-blue">100 N/m</text>

        
        <line x1="240" y1="20" x2="240" y2="35" stroke="#475569" stroke-width="2" />
        <path class="spring-line sp-blue" d="M 240 35 L 230 42 L 250 54 L 230 66 L 250 78 L 230 90 L 250 102 L 230 114 L 240 120" />
        <line x1="240" y1="120" x2="240" y2="135" stroke="#475569" stroke-width="2" />
        <text x="240" y="78" class="tag-bubble tag-blue">100 N/m</text>

        
        <rect x="145" y="135" width="110" height="6" rx="2" class="fixture" />

        
        <line x1="200" y1="141" x2="200" y2="155" stroke="#475569" stroke-width="2" />
        <path class="spring-line sp-green" d="M 200 155 L 188 163 L 212 177 L 188 191 L 212 205 L 188 219 L 212 233 L 188 247 L 200 255" />
        <line x1="200" y1="255" x2="200" y2="270" stroke="#475569" stroke-width="2" />
        <text x="200" y="205" class="tag-bubble tag-green">200 N/m</text>

        
        <rect x="180" y="270" width="40" height="24" class="load-mass" />
        <text x="200" y="283" font-size="11" font-weight="700" fill="#475569" text-anchor="middle" dominant-baseline="central">LOAD</text>
      </g>

      
      <g id="stage2" class="network-group hidden">
        
        <path d="M 140 30 L 130 30 L 130 260 L 140 260" class="bracket" />
        <text x="75" y="145" class="formula-tag">Series<tspan x="75" dy="16" font-weight="700" fill="#7c3aed">¹/ₖ = ¹/₂₀₀ + ¹/₂₀₀</tspan></text>

        
        <line x1="200" y1="20" x2="200" y2="35" stroke="#475569" stroke-width="2" />
        <path class="spring-line sp-purple" d="M 200 35 L 188 43 L 212 57 L 188 71 L 212 85 L 188 99 L 212 113 L 188 127 L 200 135" />
        <line x1="200" y1="135" x2="200" y2="148" stroke="#475569" stroke-width="2" />
        <text x="200" y="85" class="tag-bubble tag-purple">200 N/m</text>

        
        <circle cx="200" cy="148" r="4" fill="#475569" />

        
        <line x1="200" y1="148" x2="200" y2="160" stroke="#475569" stroke-width="2" />
        <path class="spring-line sp-green" d="M 200 160 L 188 168 L 212 182 L 188 196 L 212 210 L 188 224 L 212 238 L 188 252 L 200 260" />
        <line x1="200" y1="260" x2="200" y2="270" stroke="#475569" stroke-width="2" />
        <text x="200" y="210" class="tag-bubble tag-green">200 N/m</text>

        
        <rect x="180" y="270" width="40" height="24" class="load-mass" />
        <text x="200" y="283" font-size="11" font-weight="700" fill="#475569" text-anchor="middle" dominant-baseline="central">LOAD</text>
      </g>

      
      <g id="stage3" class="network-group hidden">
        
        <line x1="200" y1="20" x2="200" y2="45" stroke="#475569" stroke-width="2" />
        <path class="spring-line sp-amber" d="M 200 45 L 185 57 L 215 77 L 185 97 L 215 117 L 185 137 L 215 157 L 185 177 L 215 197 L 185 217 L 215 237 L 185 253 L 200 265" />
        <line x1="200" y1="265" x2="200" y2="270" stroke="#475569" stroke-width="2" />

        <text x="200" y="145" class="tag-bubble tag-amber" font-size="15">k_total = 100 N/m</text>

        
        <rect x="180" y="270" width="40" height="24" class="load-mass" />
        <text x="200" y="283" font-size="11" font-weight="700" fill="#475569" text-anchor="middle" dominant-baseline="central">LOAD</text>
      </g>
    </svg>
  </div>

  <script>
    const stages = [
      document.getElementById('stage1'),
      document.getElementById('stage2'),
      document.getElementById('stage3')
    ];
    const buttons = document.querySelectorAll('.btn-step');
    const playBtn = document.getElementById('playBtn');

    let currentStep = 0;
    let isPlaying = true;
    let timer = null;

    function setStep(idx) {
      currentStep = idx;
      stages.forEach((stg, i) => {
        if (i === idx) {
          stg.classList.remove('hidden');
        } else {
          stg.classList.add('hidden');
        }
      });

      buttons.forEach((btn, i) => {
        btn.classList.toggle('active', i === idx);
      });
    }

    function nextStep() {
      const next = (currentStep + 1) % stages.length;
      setStep(next);
    }

    function startTimer() {
      stopTimer();
      timer = setInterval(nextStep, 3500);
      isPlaying = true;
      playBtn.textContent = '⏸';
    }

    function stopTimer() {
      if (timer) {
        clearInterval(timer);
        timer = null;
      }
      isPlaying = false;
      playBtn.textContent = '▶';
    }

    buttons.forEach((btn) => {
      btn.addEventListener('click', () => {
        const stepIdx = parseInt(btn.dataset.step, 10);
        setStep(stepIdx);
        if (isPlaying) startTimer(); // reset interval
      });
    });

    playBtn.addEventListener('click', () => {
      if (isPlaying) {
        stopTimer();
      } else {
        nextStep();
        startTimer();
      }
    });

    // Start auto loop
    startTimer();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      user-select: none;
    }

    .panels {
      display: flex;
      flex-direction: row;
      justify-content: center;
      align-items: stretch;
      gap: 16px;
      width: 100%;
      max-width: 640px;
      flex: 1;
    }

    .panel {
      flex: 1;
      min-width: 0;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      position: relative;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 8px;
    }

    svg {
      width: 100%;
      height: 100%;
      max-height: 320px;
      overflow: visible;
    }

    .controls {
      width: 100%;
      max-width: 480px;
      display: flex;
      align-items: center;
      gap: 12px;
      margin-top: 10px;
      background: #f8fafc;
      padding: 8px 16px;
      border-radius: 20px;
      border: 1px solid #e2e8f0;
    }

    .controls label {
      font-size: 13px;
      font-weight: 600;
      color: #1e2945;
      white-space: nowrap;
    }

    input[type=range] {
      flex: 1;
      accent-color: #22b7ff;
      cursor: pointer;
    }

    .val-badge {
      font-size: 13px;
      font-weight: 700;
      color: #22b7ff;
      min-width: 45px;
      text-align: right;
    }

    @media (max-width: 480px) {
      body { padding: 6px; }
      .panels { gap: 8px; }
      .controls { padding: 6px 12px; }
    }
  </style>
</head>
<body>

  <div class="panels">
    
    <div class="panel">
      <svg id="springSvg" viewBox="0 0 200 280">
        <defs>
          <marker id="arrow-green" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#16a34a"/>
          </marker>
          <marker id="arrow-red" viewBox="0 0 10 10" refX="5" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse">
            <path d="M 0 1.5 L 8 5 L 0 8.5 z" fill="#dc2626"/>
          </marker>
        </defs>

        
        <rect x="30" y="10" width="140" height="8" fill="#cbd5e1" rx="2"/>
        <line x1="30" y1="18" x2="170" y2="18" stroke="#94a3b8" stroke-width="2"/>
        <line x1="45" y1="10" x2="35" y2="18" stroke="#94a3b8" stroke-width="1.5"/>
        <line x1="75" y1="10" x2="65" y2="18" stroke="#94a3b8" stroke-width="1.5"/>
        <line x1="105" y1="10" x2="95" y2="18" stroke="#94a3b8" stroke-width="1.5"/>
        <line x1="135" y1="10" x2="125" y2="18" stroke="#94a3b8" stroke-width="1.5"/>
        <line x1="165" y1="10" x2="155" y2="18" stroke="#94a3b8" stroke-width="1.5"/>

        
        <line x1="15" y1="105" x2="185" y2="105" stroke="#94a3b8" stroke-width="1.5" stroke-dasharray="4,4"/>
        <text x="185" y="101" fill="#64748b" font-size="11" font-weight="600" text-anchor="end">x = 0</text>

        
        <path id="springPath" fill="none" stroke="#22b7ff" stroke-width="3.5" stroke-linecap="round" stroke-linejoin="round"/>

        
        <g id="dispIndicator">
          <line id="dispLine" x1="45" y1="105" x2="45" y2="105" stroke="#1e2945" stroke-width="1.5"/>
          <path id="dispCapTop" d="M 40 105 L 50 105" stroke="#1e2945" stroke-width="1.5"/>
          <path id="dispCapBottom" d="M 40 105 L 50 105" stroke="#1e2945" stroke-width="1.5"/>
          <text id="dispText" x="38" y="110" fill="#1e2945" font-size="12" font-weight="700" text-anchor="end">x</text>
        </g>

        
        <g id="massGroup">
          <rect id="massBox" x="80" y="90" width="40" height="30" rx="4" fill="#3b82f6"/>
          <text id="massLabel" x="100" y="110" fill="#ffffff" font-size="12" font-weight="bold" text-anchor="middle">m</text>
        </g>

        
        
        <line id="forceRest" x1="140" y1="105" x2="140" y2="75" stroke="#16a34a" stroke-width="3" marker-end="url(#arrow-green)"/>
        <text id="labelRest" x="148" y="85" fill="#16a34a" font-size="11" font-weight="700">Fs</text>

        
        <line id="forceExt" x1="140" y1="105" x2="140" y2="135" stroke="#dc2626" stroke-width="3" marker-end="url(#arrow-red)"/>
        <text id="labelExt" x="148" y="130" fill="#dc2626" font-size="11" font-weight="700">Fext</text>
      </svg>
    </div>

    
    <div class="panel">
      <svg id="graphSvg" viewBox="0 0 200 280">
        
        
        <line x1="35" y1="240" x2="35" y2="25" stroke="#64748b" stroke-width="2"/>
        <polygon points="35,20 31,28 39,28" fill="#64748b"/>
        <text x="35" y="14" fill="#1e2945" font-size="12" font-weight="700" text-anchor="middle">F (N)</text>

        
        <line x1="35" y1="240" x2="185" y2="240" stroke="#64748b" stroke-width="2"/>
        <polygon points="190,240 182,236 182,244" fill="#64748b"/>
        <text x="185" y="258" fill="#1e2945" font-size="12" font-weight="700" text-anchor="end">x (m)</text>

        <text x="26" y="244" fill="#64748b" font-size="10" text-anchor="end">0</text>

        
        <line x1="35" y1="135" x2="175" y2="135" stroke="#e2e8f0" stroke-width="1" stroke-dasharray="2,2"/>
        <line x1="105" y1="240" x2="105" y2="35" stroke="#e2e8f0" stroke-width="1" stroke-dasharray="2,2"/>

        
        <line x1="35" y1="240" x2="175" y2="40" stroke="#cbd5e1" stroke-width="2.5" stroke-linecap="round"/>

        
        <path d="M 95 154 L 135 154 L 135 97" fill="none" stroke="#22b7ff" stroke-width="1.5" stroke-dasharray="2,2"/>
        <text x="142" y="130" fill="#0284c7" font-size="11" font-weight="700">Slope = k</text>

        
        <line id="graphActiveLine" x1="35" y1="240" x2="35" y2="240" stroke="#22b7ff" stroke-width="3.5" stroke-linecap="round"/>

        
        <line id="projY" x1="35" y1="240" x2="35" y2="240" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2"/>
        <line id="projX" x1="35" y1="240" x2="35" y2="240" stroke="#94a3b8" stroke-width="1" stroke-dasharray="2,2"/>

        
        <circle id="graphDot" cx="35" cy="240" r="5" fill="#22b7ff" stroke="#ffffff" stroke-width="2"/>
      </svg>
    </div>
  </div>

  
  <div class="controls">
    <label for="dispSlider">Hanging Load:</label>
    <input type="range" id="dispSlider" min="0" max="100" value="45" step="1">
    <div class="val-badge" id="loadVal">0.45x</div>
  </div>

  <script>
    const slider = document.getElementById('dispSlider');
    const springPath = document.getElementById('springPath');
    const massGroup = document.getElementById('massGroup');
    const massBox = document.getElementById('massBox');
    const forceRest = document.getElementById('forceRest');
    const labelRest = document.getElementById('labelRest');
    const forceExt = document.getElementById('forceExt');
    const labelExt = document.getElementById('labelExt');
    const dispLine = document.getElementById('dispLine');
    const dispCapBottom = document.getElementById('dispCapBottom');
    const dispText = document.getElementById('dispText');
    const graphActiveLine = document.getElementById('graphActiveLine');
    const graphDot = document.getElementById('graphDot');
    const projX = document.getElementById('projX');
    const projY = document.getElementById('projY');
    const loadVal = document.getElementById('loadVal');

    const EQ_Y = 105; // Y position of top of mass at equilibrium
    const TOP_Y = 18;  // Ceiling attachment point

    function generateSpringPath(yStart, yEnd, coils, width) {
      const totalLen = yEnd - yStart;
      const step = totalLen / (coils * 2);
      let d = `M 100 ${yStart} L 100 ${yStart + 6}`;
      
      let curY = yStart + 6;
      const coilLen = totalLen - 12;
      const coilStep = coilLen / (coils * 2);

      for (let i = 0; i < coils * 2; i++) {
        curY += coilStep;
        const x = (i % 2 === 0) ? (100 + width) : (100 - width);
        d += ` L ${x} ${curY}`;
      }
      d += ` L 100 ${yEnd}`;
      return d;
    }

    function update(val) {
      const norm = val / 100; // 0 to 1
      loadVal.textContent = (norm * 1.0).toFixed(2) + ' m';

      // Physical stretch
      const maxStretch = 100;
      const stretch = norm * maxStretch;
      const curMassTop = EQ_Y + stretch;

      // Update spring coil
      springPath.setAttribute('d', generateSpringPath(TOP_Y, curMassTop, 6, 14));

      // Update mass box
      const massHeight = 24 + norm * 16;
      massBox.setAttribute('y', curMassTop);
      massBox.setAttribute('height', massHeight);
      document.getElementById('massLabel').setAttribute('y', curMassTop + massHeight / 2 + 4);

      // Update displacement bracket
      if (stretch > 3) {
        dispLine.setAttribute('y2', curMassTop);
        dispCapBottom.setAttribute('d', `M 40 ${curMassTop} L 50 ${curMassTop}`);
        dispText.setAttribute('y', EQ_Y + stretch / 2 + 4);
        dispLine.style.display = '';
        dispCapBottom.style.display = '';
        dispText.style.display = '';
      } else {
        dispLine.style.display = 'none';
        dispCapBottom.style.display = 'none';
        dispText.style.display = 'none';
      }

      // Update Force vectors
      const centerMassY = curMassTop + massHeight / 2;
      const forceLen = 12 + norm * 48;

      forceRest.setAttribute('x1', 145);
      forceRest.setAttribute('x2', 145);
      forceRest.setAttribute('y1', centerMassY);
      forceRest.setAttribute('y2', centerMassY - forceLen);
      labelRest.setAttribute('y', centerMassY - forceLen - 4);
      labelRest.setAttribute('x', 140);

      forceExt.setAttribute('x1', 145);
      forceExt.setAttribute('x2', 145);
      forceExt.setAttribute('y1', centerMassY);
      forceExt.setAttribute('y2', centerMassY + forceLen);
      labelExt.setAttribute('y', centerMassY + forceLen + 12);
      labelExt.setAttribute('x', 140);

      // Update Graph
      const gStartX = 35, gStartY = 240;
      const gEndX = 175, gEndY = 40;
      const currGX = gStartX + norm * (gEndX - gStartX);
      const currGY = gStartY - norm * (gStartY - gEndY);

      graphActiveLine.setAttribute('x2', currGX);
      graphActiveLine.setAttribute('y2', currGY);

      graphDot.setAttribute('cx', currGX);
      graphDot.setAttribute('cy', currGY);

      projX.setAttribute('x1', currGX);
      projX.setAttribute('y1', currGY);
      projX.setAttribute('x2', currGX);
      projX.setAttribute('y2', gStartY);

      projY.setAttribute('x1', currGX);
      projY.setAttribute('y1', currGY);
      projY.setAttribute('x2', gStartX);
      projY.setAttribute('y2', currGY);
    }

    slider.addEventListener('input', (e) => {
      update(parseFloat(e.target.value));
    });

    update(parseFloat(slider.value));
  </script>
</body>
</html>

Propiedades fundamentales de los fluidos: densidad y presión

Presión hidrostática y principio fundamental de la hidrostática

Principio de Pascal y prensas hidráulicas

Sistemas de frenos hidráulicos en vehículos

Principio de Arquímedes y fuerza de empuje

Flotabilidad en ingeniería naval y submarinos

Globos aerostáticos y flotación en gases

science

Hidrostática y flotación: principios y aplicaciones

Tensile and Compressive Stress Calculations

Tensile Strain and Fractional Deformation

The Young Modulus and Material Stiffness

Experimental Determination of the Young Modulus

Stress-Strain Curves and Critical Material Points

Classifying Ductile, Brittle, and Polymeric Materials

Mechanical Properties: Stress, Strain, and the Young Modulus

Hooke's Law and Spring Combinations

Force-Extension Graphs for Materials and Polymers

Elastic Strain Energy and Spring Deformation

Calculating Work Done in Stretching from Force-Extension Graphs

Plastic Deformation and Elastic Hysteresis

Strain Energy Density and Energy Absorption

Force-Extension Graphs, Hooke's Law, and Stored Elastic Energy

Dinámica de fluidos: caudal y ecuación de continuidad

Ecuación de Bernoulli y conservación de energía en fluidos

Efecto Venturi y medidores de flujo

Sustentación aerodinámica en alas de aviones

Viscosidad y flujo laminar versus turbulento

Oleoductos y redes de distribución de agua potable

Sistemas neumáticos en la automatización industrial

Hemodinámica: mecánica de fluidos en el sistema cardiovascular

Hidrodinámica y aplicaciones tecnológicas

Tensile Stress, Strain, and Young Modulus Calculations

Stress-Strain Graphs: Elastic Limit and Plastic Deformation

Elastic Strain Energy and Hysteresis Loops

Hydrostatic Pressure and Archimedes' Principle

Fluid Continuity Equation in Laminar Flow

Bernoulli's Principle and Fluid Flow Applications

Solid Mechanics and Fluid Dynamics

Dinámica en planos inclinados sin fricción

Dinámica en planos inclinados con fricción

Sistemas de cuerpos conectados y poleas

Fuerza elástica y ley de Hooke

Fuerza centrípeta y dinámica circular

Fuerzas de resistencia en fluidos y velocidad terminal

Fuerzas aparentes e inerciales en marcos acelerados

Dinámica del movimiento oscilatorio en sistemas masa-resorte

Aplicaciones de la dinámica newtoniana

Densidad, peso específico y gravedad específica de fluidos

Presión en fluidos y fuerza hidrostática

Presión atmosférica, barómetros y manómetros en U

Condiciones de flotabilidad y peso aparente

Tensión superficial y capilaridad en líquidos

Hidrostática: presión, flotación y fenómenos superficiales

Líneas de corriente, flujo laminar y caudal volumétrico

Ecuación de continuidad en fluidos incompresibles

Ecuación de Bernoulli: conservación de energía en fluidos

Efecto Venturi y teorema de Torricelli

Sustentación aerodinámica y efecto Magnus

Viscosidad de fluidos reales y ley de Poiseuille

Fluidos en sistemas biológicos e ingeniería hidráulica

Hidrodinámica: flujo, Bernoulli y aplicaciones

Propiedades físicas de los fluidos biológicos: cohesión y tensión superficial

OGS.13.PS.4

Aligned learning resources

Related diagrams