Dimensional analysis for simple pendulum period (Period depends on length and gravity as √(l/g) up to)
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Period depends on length and gravity as √(l/g) up to a dimensionless constant k (2π from physics, not from dimensions alone).
What each symbol means
| Symbol | What it stands for |
|---|---|
| T | Period |
| g | Acceleration due to gravity |
| k | Dimensionless constant |
| l | Length |
When to use this
Assumes dependence only on l and g; angle small so amplitude not in leading scaling.