角度-时间
读数
发生了什么
重力提供一个与 sin(θ) 成正比的回复力矩。角度小时 sin(θ) ≈ θ，于是得到简谐运动，周期 T = 2π√(L/g)。初始角度大时，实测周期会比小角度公式略长。摆长加倍并不会让周期加倍，而是乘以 √2，因为 T 随 L 的平方根增大。
- Period of a pendulumT = 2π √(L / g)
考试大纲
- A-Level Physics AQA 3.6.2, OCR, Edexcelsimple harmonic motion and the simple pendulum
- GCSE Physicsrequired practical skills on timing oscillations
挑战
先预测：要让周期加倍，摆线要长多少？在两个长度下测量来验证你的答案。
摆线要长到原来的四倍：T 随 √L 增大，所以周期加倍需要 4 倍的长度。
系统地学
GCSE Combined and Separate Science 中讲这个主题的课：先看分步讲解，再做考试风格的题目，每次数字都不同。 课程为英文。
常见问题
Does the mass of a pendulum change its period?
No. A heavier bob needs more force to accelerate, but gravity pulls it harder in exactly the same proportion, so the period T = 2π√(L/g) has no mass in it.
Why is the period longer at big angles?
The formula uses sin θ ≈ θ, which only holds for small angles. At larger angles the restoring force is weaker than the approximation assumes, so each swing takes a little longer: about 3% longer at 40°.
How long is a pendulum with a period of 2 seconds?
L = g(T/2π)², so on Earth L = 9.81 × (2/2π)² ≈ 0.994 m. That is the classic seconds pendulum.
How do I find g from a pendulum experiment?
Time many swings, divide to get one period, then use g = 4π²L/T². A 0.800 m pendulum with T = 1.795 s gives g = 4π² × 0.800 / 1.795² = 9.80 m/s². Pick Gravity g under Solve for to see each step, and keep the swing small so the formula holds.