spring-forces-hooke-s-law
Spring Forces and Hooke's Law in Mechanics (Dynamics). Theoretical foundations, governing equations, analytical problem-solving methods, and typical archetypes.
- License 许可
- MIT
- 最近更新
- 2026-10-17
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- ★ 8
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01 前言 Front Matter
- name
- spring-forces-hooke-s-law
- metadata
- { "id": "mech.dynamics.springs", "domain": "Mechanics", "subdomain": "Dynamics", "difficulty": "2/5" }
- description
- Spring Forces and Hooke's Law in Mechanics (Dynamics). Theoretical foundations, governing equations, analytical problem-solving methods, and typical archetypes.
02 资源文件 1
- 参考文档metadata.json1.0 KB
03 SKILL.md 正文
Spring Forces and Hooke's Law
ID: mech.dynamics.springs
Domain: Mechanics → Dynamics
Difficulty: 2/5
Prerequisites
- mech.dynamics.newton_laws
Core Concepts
- Hooke's law
- spring constant
- restoring force
- series/parallel springs
- effective k
Key Equations
$$ F = -kx $$ $$ \frac{1}{k_{eff}} = \sum_i \frac{1}{k_i}\ \text{(series)} $$ $$ k_{eff} = \sum_i k_i\ \text{(parallel)} $$
Methods
- Set x = 0 at the equilibrium position
- Write ma = -kx
- Combine springs when needed
Typical Problem Types
- Mass on a spring
- Springs in series/parallel
- Coupled oscillators
Common Pitfalls
- Forgetting the minus sign in Hooke's law
- Using the wrong effective k
Related Skills
- mech.oscillations.shm
- mech.energy.conservative_potential
References
- Halliday-Resnick-Walker Ch.7,15
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