PhysicsChapter 3: Simple Harmonic Motion
Mass-Spring System
A mass-spring system
Definition
A mass-spring system consists of a mass attached to an elastic spring which can perform SHM when the spring obeys Hooke's law and damping is negligible.
Dependence
Hooke's law: F = −kx Using Newton's second law: F = ma Therefore: ma = −kx or: a = −(km)x Compare with: a = −ω²x Thus: ω² = km and: ω = √(km) Therefore: T = 2π√(m/k) and: f = (1/2π)√(km) Increasing mass increases period. Increasing spring constant decreases period. Amplitude does not affect period for an ideal linear spring.
Formula / Key Relation
**F=-kx ω=√(km) T=2π√(m/k) f=(1/2π)√(km)**
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Review the key facts, formulas and checks before you move on.Mass-Spring System
Sticky Notes · Quick Revision
`m ↑ → T ↑`
- `k ↑ → T ↓`
60-second revision
- Spring SHM follows directly from Hooke's law.
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