PhysicsChapter 3: Simple Harmonic Motion
Simple Pendulum
A simple pendulum
Definition
A simple pendulum consists ideally of a point mass suspended by a light inextensible string which performs approximately SHM for small angular displacements.
Important Results
For pendulum length `L` and angular displacement `θ`, the restoring component of weight is: F = −mg sinθ For small angles measured in radians: sinθ ≈ θ Since: x ≈ Lθ the restoring effect becomes proportional to displacement. Therefore the small-angle pendulum performs approximate SHM. Angular frequency: ω = √(g/L) Period: T = 2π√(Lg) Frequency: f=(1/2π)√(g/L) Period increases with pendulum length. Period decreases when g increases. For small oscillations, period is approximately independent of mass.
Formula / Key Relation
**T=2π√(Lg) ω=√(g/L)**
Exam preparation
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Review the key facts, formulas and checks before you move on.Simple Pendulum
Sticky Notes · Quick Revision
`T ∝ √L`
- `T ∝ 1/√g`
- Mass → no effect on ideal small-angle T
60-second revision
- A small-angle simple pendulum approximately performs SHM.
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