📚 Physics for the IB Diploma 396: Simple Pendulum Investigation | IB物理教材396页实验探究：单摆
Physics for the IB Diploma, by K.A. Tsokos, is a cornerstone resource for IB Physics students. On page 396, a practical investigation invites learners to explore the relationship between the length of a simple pendulum and its period, and to determine the acceleration due to gravity, g. This classic experiment develops crucial skills in experimental design, data analysis, and evaluation that directly align with the IB Internal Assessment criteria.
《Physics for the IB Diploma》是IB物理学生的核心教材。该书第396页提供了一个实验探究，引导学生探究单摆长度与周期之间的关系，并测定重力加速度g。这一经典实验有助于学生培养实验设计、数据分析和评估的关键技能，与IB内部评估标准高度契合。
1. Introduction to Experiment 396 | 实验396简介
The investigation on page 396 is not just a routine lab; it is a microcosm of the scientific process demanded by the IB. Students are expected to formulate a focused research question, control variables, collect precise data, and critically evaluate their findings. The simple pendulum serves as an ideal system to study simple harmonic motion and error propagation. It also draws a direct line to the IA criteria, making it an excellent preparatory task.
第396页的实验探究并非一次普通实验，而是IB所要求的科学探究过程的缩影。学生需要提出明确的研究问题，控制变量，收集精确数据，并批判性地评估结果。单摆是研究简谐运动与误差传递的理想系统，也与IA标准直接关联，是绝佳的预备练习。
2. Theory of the Simple Pendulum | 单摆理论
For small amplitudes (typically less than 10°), the simple pendulum approximates simple harmonic motion. The period T is given by the equation:
对于小幅度（通常小于10°），单摆可近似为简谐运动。其周期T由下式给出：
T = 2π√L/g
where L is the length of the pendulum and g is the gravitational field strength. By squaring both sides, we obtain a linear relationship:
其中L为摆长，g为重力加速度。两边平方后，得到线性关系：
T² = (4π²/g) × L
ermined from the gradient. The model also assumes the string is massless, inextensible, and the bob is a point mass, which will be evaluated later.
因此，绘制T²关于L的图像会得到一条过原点的直线，斜率=4π²/g。通过梯度即可求得g值。该模型还假设细绳无质量、不可伸长，且摆球为点质量，这些将在后文评估。
3. Research Question and Hypothesis | 研究问题与假设
The core research question is: 'How does the period T of a simple pendulum depend on its length L?' g calculation of g. Additionally, we predict the graph will pass through the origin as T = 0 when L = 0.
核心研究问题是：“单摆的周期T如何取决于其长度L？”基于理论模型，我们假设T与√L成正比，且T²-L图为线性，可用来计算g。此外，我们预测该图像过原点，因为当L=0时T=0。
4. Identification of Variables | 变量识别
For a reliable investigation, variables must be clearly identified. The independent variable is the length L of the pendulum, measured from the point of suspension to the centre of the bob. The dependent variable is the period T, determined by measuring the time for a number of oscillations and dividing by the count. Control variables include the amplitude (kept small, e.g. <10°), the mass of the bob, and the environmental conditions (avoid drafts, use the same setup). It is essential to use the same bob throughout to eliminate mass as a confounding factor.
为确保探究可靠，必须清晰识别变量。自变量是摆长L，从悬点到摆球中心测量。因变量是周期T，通过测量多次摆动的时间并除以次数确定。控制变量包括振幅（保持较小，如<10°）、摆球质量以及环境条件（避免气流，使用同一装置）。全程使用同一摆球至关重要，以消除质量这一干扰因素。
5. Apparatus and Setup | 仪器与装置
Typical apparatus includes a sturdy stand and clamp, a light inextensible string, a small dense spherical bob (e.g. a metal ball with a hook), a metre ruler or tape measure, a protractor (to ensure small angle release), and a digital stopwatch. A reference point should be marked at the equilibrium position to time oscillations accurately. For more precise work, a photogate can replace the stopwatch, but page 396 encourages using simple tools to understand measurement limitations.
典型装置包括稳固的铁架台和夹具、轻质不可伸长的细绳、小而密实的球形摆球（如带钩金属球）、米尺或卷尺、量角器（确保小角度释放）以及电子秒表。需在平衡位置标记参考点，以准确计时摆动。对于更精确的探究，光电门可替代秒表，但第396页鼓励使用简单工具，以理解测量局限性。
6. Data Collection Procedure | 数据收集步骤
re the string is vertical and taut. Displace the bob by an angle less than 10° and release it smoothly. Using the stopwatch, measure the time for 20 complete oscillations (t₂₀). Repeat this measurement three times for each length to reduce random error. Then calculate the average period T by using T = t₂₀/20. Decrease L in steps (e.g. 0.90 m, 0.80 m, ..., down to about 0.30 m) and record data in a prepared table.
首先设置摆长约1.00米的单摆。用米尺测量从夹具点到摆球中心的长度L。确保绳子垂直且拉紧。将摆球位移小于10°，平稳释放。使用秒表测量20次完整摆动的时间（t₂₀）。每个长度重复测量三次以减小随机误差。然后通过T = t₂₀/20计算平均周期。逐步减小L（如0.90 m、0.80 m……至约0.30 m），并将数据记录在准备好的表格中。
A sample data table should include columns for length L (m), time for 20 oscillations (s) for trial 1, 2, 3, mean t₂₀ (s), period T (s), and T² (s²). Record data to an appropriate number of significant figures, reflecting the precision of instruments.
示例数据表应包括以下列：长度L (m)、20次摆动时间（s）（试验1、2、3
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