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🕰️ 单摆周期计算器Pendulum Period Calculator
由摆长和重力加速度计算单摆周期 T = 2π√(L/g) 和频率，并可按摆角给出大摆角下的精确周期（算术–几何平均法）；也能由周期反求摆长。Calculate a simple pendulum's period T = 2π√(L/g) and frequency from its length and gravity, with the exact large-amplitude period for a given swing angle (via the arithmetic–geometric mean) — or work back from a period to the length.
使用说明与常见问题How-to & FAQ
「单摆周期计算器」是什么？What is the Pendulum Period Calculator tool?
由摆长和重力加速度计算单摆周期 T = 2π√(L/g) 和频率，并可按摆角给出大摆角下的精确周期（算术–几何平均法）；也能由周期反求摆长。Calculate a simple pendulum's period T = 2π√(L/g) and frequency from its length and gravity, with the exact large-amplitude period for a given swing angle (via the arithmetic–geometric mean) — or work back from a period to the length.
如何使用「单摆周期计算器」？How do I use the Pendulum Period Calculator tool?
在「单摆周期计算器」中，填写「求」、「摆长 L（米）」、「周期 T（秒）」、「摆角 θ₀（度，0 为小角近似）」、「重力加速度 g（m/s²）」等参数，结果会随输入实时计算并显示在下方。In the Pendulum Period Calculator: Fill in "Solve for", "Length L (m)", "Period T (s)", "Amplitude θ₀ (degrees, 0 = small-angle)", "Gravity g (m/s²)"; results are recalculated instantly as you type.
单摆周期公式是什么？What is the pendulum period formula?
小摆角时 T = 2π√(L/g)，与摆锤质量无关。例如 1 米长的摆在标准重力 9.80665 m/s² 下周期约 2.0064 秒，所以约 0.994 米的摆每摆一次（单程）约 1 秒，即「秒摆」。For small swings T = 2π√(L/g), independent of the bob's mass. A 1 m pendulum under standard gravity 9.80665 m/s² has a period of about 2.0064 s, so a pendulum about 0.994 m long takes about 1 s per one-way swing — the 'seconds pendulum'.
摆角大时怎么算？What about large swings?
摆角大时周期变长。精确周期 T = T₀ ÷ AGM(1, cos(θ₀/2))，AGM 是算术–几何平均，本工具直接迭代计算。30° 时约长 1.74%，90° 时约长 18%。Larger swings take longer. The exact period is T = T₀ ÷ AGM(1, cos(θ₀/2)), where AGM is the arithmetic–geometric mean, which the tool iterates directly. At 30° the period is about 1.74% longer, at 90° about 18% longer.
有哪些假设？What does it assume?
理想单摆：摆线无质量且不可伸长、摆锤是质点、没有空气阻力和摩擦。实际的复摆（如摆杆有质量）需要用转动惯量计算。An ideal simple pendulum: a massless, inextensible string, a point-mass bob and no air resistance or friction. A real compound pendulum (such as a heavy rod) needs its moment of inertia.
计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?
「单摆周期计算器」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Pendulum Period Calculator uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.
「单摆周期计算器」免费吗？需要注册吗？Is the Pendulum Period Calculator free? Do I need an account?
「单摆周期计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Pendulum Period Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.