位移-时间
读数
发生了什么
弹簧的回复力为 −kx，所以加速度与位移成正比，并指向平衡位置，这正是简谐运动的定义。周期 2π√(m/k) 与振幅无关。阻尼每个周期都会带走能量，让振动呈指数衰减，但周期基本不变。
- Period of a mass on a springT = 2π √(m / k)
- Hooke's lawF = −kx
考试大纲
- GCSE Physics AQA 4.5.3Hooke's law F = kx
- A-Level Physics AQA 3.6.2simple harmonic motion, damping and resonance
挑战
先预测：质量变为四倍时，周期会怎样？分别用 m 和 4m 运行，比较图表。
质量变为四倍，周期加倍，因为 T ∝ √m。
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
What is the period of a mass on a spring?
T = 2π√(m/k). A heavier mass or a softer spring gives slower oscillations; the amplitude does not change the period.
What is Hooke's law?
The force from a spring is proportional to its extension, F = kx, as long as it is not stretched past its limit of proportionality. k is the spring constant in N/m.
What does damping do?
Damping removes energy every cycle, so the amplitude shrinks exponentially. Light damping barely changes the period; heavy damping can stop the oscillation altogether.
How do I find the spring constant from the period?
Rearrange T = 2π√(m/k) to k = 4π²m/T². A 0.50 kg mass bouncing with a period of 0.80 s gives k = 4π² × 0.50 / 0.80² = 30.8 N/m. Pick Spring constant under Solve for to see each step, or k from a stretch to use Hooke's law instead.