783 lines
50 KiB
HTML
783 lines
50 KiB
HTML
<!DOCTYPE html>
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||
<html lang="zh">
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<head>
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<meta charset="UTF-8">
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<meta name="viewport" content="width=device-width, initial-scale=1.0">
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<title>单摆实验重力加速度测量分析</title>
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<script src="https://cdn.tailwindcss.com"></script>
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</head>
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<div id="artifacts-component-root-react"
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class="min-h-full w-full">
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<div class="p-4 bg-gray-50 min-h-screen">
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<div class="max-w-6xl mx-auto">
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<h1 class="text-3xl font-bold text-center mb-6 text-blue-800">
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单摆实验重力加速度测量分析</h1>
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<div class="bg-white p-6 rounded-lg shadow-md mb-8">
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<h2 class="text-xl font-semibold mb-4 text-blue-700">实验摘要</h2>
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<div class="grid grid-cols-1 md:grid-cols-2 gap-4">
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<div class="bg-blue-50 p-4 rounded-lg">
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<h3 class="font-medium text-blue-800 mb-2">平均重力加速度</h3>
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<p class="text-2xl font-bold">9.7576 ± 0.0147 m/s²</p>
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<p class="text-sm text-gray-600">从四次实验计算的平均值（95%置信区间）
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</p>
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<p class="text-sm text-gray-500 mt-2">标准差: 0.0147 m/s²
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</p>
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<p class="text-sm text-gray-500">相对标准值误差: 0.43%</p>
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<div class="mt-2 text-xs text-gray-500">
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<p>计算方法: σ = √[Σ(x_i - x̄)² / (n-1)]</p>
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<p>g₁ = 9.7498, g₂ = 9.7746, g₃ = 9.7411, g₄ =
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9.7650</p>
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<p>平均值 = (g₁+g₂+g₃+g₄)/4 = 9.7576 m/s²</p>
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</div>
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</div>
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<div class="bg-green-50 p-4 rounded-lg">
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<h3 class="font-medium text-green-800 mb-2">线性拟合计算的重力加速度
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</h3>
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<p class="text-2xl font-bold">9.9063 ± 0.0121 m/s²</p>
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<p class="text-sm text-gray-600">从T²与L的线性关系计算（基于拟合误差）
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</p>
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<p class="text-sm text-gray-500 mt-2">拟合标准误差: 0.0017</p>
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<p class="text-sm text-gray-500">相对标准值误差: 1.08%</p>
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<div class="mt-2 text-xs text-gray-500">
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<p>计算方法: g = 4π²/斜率</p>
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<p>斜率 = 3.9852 ± 0.0034</p>
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<p>拟合优度 R² = 1.0000</p>
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</div>
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</div>
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</div>
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<div class="mt-4 p-4 bg-yellow-50 rounded-lg">
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<h3 class="font-medium text-yellow-800 mb-2">拟合方程</h3>
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<p class="text-lg">T² = 3.9852L + 0.0404 (R² = 1.0000)</p>
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<p class="text-sm text-gray-600">根据 T² = (4π²/g)L + b 理论模型拟合
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</p>
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<p class="text-sm text-gray-500 mt-2">标准重力加速度: 9.8000 m/s²
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</p>
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<p class="text-sm text-gray-500">平均测量值与标准值比较: 9.7576 vs.
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9.8000 (Δ = 42.4 mm/s²)</p>
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</div>
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</div>
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<div class="bg-white p-6 rounded-lg shadow-md mb-8">
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<h2 class="text-xl font-semibold mb-4 text-blue-700">T² 与摆长 L
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的关系</h2>
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0.455m</tspan>
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<tspan x="463" dy="0.71em">0.52m
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<tspan x="72" dy="0.355em">1.5s²
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name="周期平方" orientation="left"
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width="60" height="206"
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class="recharts-text recharts-cartesian-axis-tick-value"
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text-anchor="end" fill="#666">
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<tspan x="72" dy="0.355em">1.8s²
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<tspan x="72" dy="0.355em">2.1s²
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<tspan x="72" dy="0.355em">2.4s²
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|
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|
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x="72" y="20"
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|
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<tspan x="72" dy="0.355em">2.7s²
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<tspan x="35" dy="0.355em">T² (s²)
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||
x="747.2095602546947"
|
||
y="49.0816499982846"
|
||
class="recharts-symbols"
|
||
transform="translate(751.7230769230767, 53.59516666666665)"
|
||
d="M4.514,0A4.514,4.514,0,1,1,-4.514,0A4.514,4.514,0,1,1,4.514,0">
|
||
</path>
|
||
</g>
|
||
</g>
|
||
</g>
|
||
</g>
|
||
</svg>
|
||
<div class="recharts-legend-wrapper"
|
||
style="position: absolute; width: 826px; height: auto; left: 20px; bottom: 40px;">
|
||
<ul class="recharts-default-legend"
|
||
style="padding: 0px; margin: 0px; text-align: center;">
|
||
<li class="recharts-legend-item legend-item-0"
|
||
style="display: inline-block; margin-right: 10px;">
|
||
<svg class="recharts-surface" width="14"
|
||
height="14" viewBox="0 0 32 32"
|
||
style="display: inline-block; vertical-align: middle; margin-right: 4px;">
|
||
<title></title>
|
||
<desc></desc>
|
||
<path fill="#8884d8" cx="16" cy="16"
|
||
class="recharts-symbols"
|
||
transform="translate(16, 16)"
|
||
d="M16,0A16,16,0,1,1,-16,0A16,16,0,1,1,16,0">
|
||
</path>
|
||
</svg><span
|
||
class="recharts-legend-item-text"
|
||
style="color: rgb(136, 132, 216);">实验数据</span>
|
||
</li>
|
||
</ul>
|
||
</div>
|
||
<div tabindex="-1"
|
||
class="recharts-tooltip-wrapper recharts-tooltip-wrapper-right recharts-tooltip-wrapper-bottom"
|
||
style="visibility: hidden; pointer-events: none; position: absolute; top: 0px; left: 0px; transform: translate(143.523px, 20px);">
|
||
<div class="recharts-default-tooltip"
|
||
style="margin: 0px; padding: 10px; background-color: rgb(255, 255, 255); border: 1px solid rgb(204, 204, 204); white-space: nowrap;">
|
||
<p class="recharts-tooltip-label"
|
||
style="margin: 0px;">摆长: 0.4040 m</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
<div class="mt-4 p-4 bg-gray-50 rounded-lg">
|
||
<p class="text-sm">根据简单摆的理论，T² 与 L 呈线性关系：T² =
|
||
(4π²/g)L，拟合线的斜率为 3.9852， 通过公式 g = 4π²/slope 计算得到重力加速度为
|
||
9.9063 m/s²。</p>
|
||
</div>
|
||
</div>
|
||
<div class="bg-white p-6 rounded-lg shadow-md mb-8">
|
||
<h2 class="text-xl font-semibold mb-4 text-blue-700">实验数据详情</h2>
|
||
<h3 class="font-medium text-blue-800 mb-2">1. 基本参数</h3>
|
||
<div class="overflow-x-auto mb-6">
|
||
<table class="min-w-full bg-white">
|
||
<thead>
|
||
<tr class="bg-blue-100">
|
||
<th class="py-2 px-4 border">实验编号</th>
|
||
<th class="py-2 px-4 border">摆长 (m)</th>
|
||
<th class="py-2 px-4 border">周期 (s)</th>
|
||
<th class="py-2 px-4 border">周期平方 (s²)</th>
|
||
<th class="py-2 px-4 border">角频率 (rad/s)</th>
|
||
<th class="py-2 px-4 border">初始振幅 (rad)</th>
|
||
<th class="py-2 px-4 border">相位 (rad)</th>
|
||
<th class="py-2 px-4 border">周期数量</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">1</td>
|
||
<td class="py-2 px-4 border text-center">0.5490
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">1.4921
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">2.2264
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">4.2111
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.1559
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">-0.5596
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">294
|
||
</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">2</td>
|
||
<td class="py-2 px-4 border text-center">0.4040
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">1.2846
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">1.6502
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">4.8911
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.3166
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">1.6707
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">273
|
||
</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">3</td>
|
||
<td class="py-2 px-4 border text-center">0.4480
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">1.3516
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">1.8268
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">4.6487
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.2821
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">-2.1701
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">273
|
||
</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">4</td>
|
||
<td class="py-2 px-4 border text-center">0.6180
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">1.5825
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">2.5043
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">3.9704
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.2183
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">-1.7966
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">360
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<h3 class="font-medium text-blue-800 mb-2">2. 阻尼参数</h3>
|
||
<div class="overflow-x-auto mb-6">
|
||
<table class="min-w-full bg-white">
|
||
<thead>
|
||
<tr class="bg-blue-100">
|
||
<th class="py-2 px-4 border">实验编号</th>
|
||
<th class="py-2 px-4 border">阻尼系数 γ (s⁻¹)</th>
|
||
<th class="py-2 px-4 border">相对阻尼系数 b/m (s⁻¹)
|
||
</th>
|
||
<th class="py-2 px-4 border">γ 的标准差</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">1</td>
|
||
<td class="py-2 px-4 border text-center">0.0023
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.0046
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.000008</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">2</td>
|
||
<td class="py-2 px-4 border text-center">0.0026
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.0051
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.000065</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">3</td>
|
||
<td class="py-2 px-4 border text-center">0.0025
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.0050
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.000023</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">4</td>
|
||
<td class="py-2 px-4 border text-center">0.0022
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">0.0044
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.000007</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<h3 class="font-medium text-blue-800 mb-2">3. 重力加速度计算</h3>
|
||
<div class="overflow-x-auto">
|
||
<table class="min-w-full bg-white">
|
||
<thead>
|
||
<tr class="bg-blue-100">
|
||
<th class="py-2 px-4 border">实验编号</th>
|
||
<th class="py-2 px-4 border">拟合得到的重力加速度 (m/s²)
|
||
</th>
|
||
<th class="py-2 px-4 border">无阻尼情况下的重力加速度 (m/s²)
|
||
</th>
|
||
<th class="py-2 px-4 border">全面修正后的重力加速度 (m/s²)
|
||
</th>
|
||
<th class="py-2 px-4 border">最大偏差 (%)</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">1</td>
|
||
<td class="py-2 px-4 border text-center">9.7355
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.7355
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.7498
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">2.24
|
||
</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">2</td>
|
||
<td class="py-2 px-4 border text-center">9.6648
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.6648
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.7746
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">4.17
|
||
</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">3</td>
|
||
<td class="py-2 px-4 border text-center">9.6815
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.6815
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.7411
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">2.48
|
||
</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">4</td>
|
||
<td class="py-2 px-4 border text-center">9.7421
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.7421
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">9.7650
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">2.13
|
||
</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
<h3 class="font-medium text-blue-800 mt-6 mb-2">4. 像素与坐标数据</h3>
|
||
<div class="overflow-x-auto">
|
||
<table class="min-w-full bg-white">
|
||
<thead>
|
||
<tr class="bg-blue-100">
|
||
<th class="py-2 px-4 border">实验编号</th>
|
||
<th class="py-2 px-4 border">摆长 (像素)</th>
|
||
<th class="py-2 px-4 border">实际摆长 (mm)</th>
|
||
<th class="py-2 px-4 border">像素到毫米转换系数</th>
|
||
<th class="py-2 px-4 border">支点坐标 X (像素)</th>
|
||
<th class="py-2 px-4 border">支点坐标 Y (像素)</th>
|
||
</tr>
|
||
</thead>
|
||
<tbody>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">1</td>
|
||
<td class="py-2 px-4 border text-center">3090.06
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">549
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.177666</td>
|
||
<td class="py-2 px-4 border text-center">1375.41
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
-2630.58</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">2</td>
|
||
<td class="py-2 px-4 border text-center">1954.91
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">404
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.206659</td>
|
||
<td class="py-2 px-4 border text-center">1270.15
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
-1675.48</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">3</td>
|
||
<td class="py-2 px-4 border text-center">2608.85
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">448
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.171723</td>
|
||
<td class="py-2 px-4 border text-center">1370.59
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
-2360.96</td>
|
||
</tr>
|
||
<tr class="hover:bg-gray-50">
|
||
<td class="py-2 px-4 border text-center">4</td>
|
||
<td class="py-2 px-4 border text-center">3413.14
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">618
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
0.181065</td>
|
||
<td class="py-2 px-4 border text-center">1458.18
|
||
</td>
|
||
<td class="py-2 px-4 border text-center">
|
||
-2939.74</td>
|
||
</tr>
|
||
</tbody>
|
||
</table>
|
||
</div>
|
||
</div>
|
||
<div class="bg-white p-6 rounded-lg shadow-md mb-8">
|
||
<h2 class="text-xl font-semibold mb-4 text-blue-700">实验分析与结论
|
||
</h2>
|
||
<div class="mb-4">
|
||
<h3 class="font-medium text-blue-800 mb-2">1. 重力加速度测量结果</h3>
|
||
<ul class="list-disc pl-6 space-y-2">
|
||
<li>四次实验测量的重力加速度平均值为 <strong>9.7576 m/s²</strong></li>
|
||
<li>通过T²与L线性关系拟合计算的重力加速度为 <strong>9.9063 m/s²</strong>
|
||
</li>
|
||
<li>理论标准值约为 9.8 m/s²，相对误差分别为 0.43% 和 -1.08%</li>
|
||
</ul>
|
||
</div>
|
||
<div class="mb-4">
|
||
<h3 class="font-medium text-blue-800 mb-2">2. 线性关系验证</h3>
|
||
<p class="mb-2">理论上，T²与L应当呈线性关系，且截距应接近于0。实验拟合得到：</p>
|
||
<ul class="list-disc pl-6 space-y-2">
|
||
<li>拟合方程: T² = 3.9852L + 0.0404</li>
|
||
<li>拟合优度 R² = 1.0000，表明数据与线性模型拟合良好</li>
|
||
<li>截距 0.0404 接近于0，符合理论预期</li>
|
||
</ul>
|
||
</div>
|
||
<div class="mb-4">
|
||
<h3 class="font-medium text-blue-800 mb-2">3. 阻尼效应分析</h3>
|
||
<ul class="list-disc pl-6 space-y-2">
|
||
<li>四次实验的阻尼系数在 0.0022 - 0.0026 s⁻¹ 范围内</li>
|
||
<li>相对阻尼系数 (b/m) 在 0.0044 - 0.0051 s⁻¹ 范围内</li>
|
||
<li>阻尼效应导致的周期修正已在实验计算中考虑</li>
|
||
</ul>
|
||
</div>
|
||
<div class="mb-4">
|
||
<h3 class="font-medium text-blue-800 mb-2">4. 误差来源分析</h3>
|
||
<ul class="list-disc pl-6 space-y-2">
|
||
<li>摆长测量误差：摆长的准确测量是影响结果的关键因素</li>
|
||
<li>大摆角效应：初始振幅的大小会影响周期，本实验中已进行修正</li>
|
||
<li>支点摩擦：可能导致额外的阻尼和能量损失</li>
|
||
<li>摆球的非点质量特性：实际摆球具有体积和转动惯量</li>
|
||
</ul>
|
||
</div>
|
||
<div>
|
||
<h3 class="font-medium text-blue-800 mb-2">5. 总结</h3>
|
||
<p>本实验通过四个不同摆长的单摆实验，得到了与理论预期相符的结果。实验中考虑了阻尼效应和大摆角修正，
|
||
测得的重力加速度与理论值接近，相对误差小于2%。T²与L的线性关系得到了很好的验证，拟合优度R²接近1，
|
||
表明实验数据质量良好。</p>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div>
|
||
</div> |