Practice

T = 2π√(L/g) Formula – Pendulum Practice

T = 2π√(L/g) — Period of a simple pendulum (small angles)

For small angles, a simple pendulum’s period is T = 2π√(L/g). It does not depend on mass or amplitude (within the small-angle limit).

Guide — how to use this formula

1. 1. Use metres for L and m/s² for g.
2. 2. T = 2π√(L/g); rearrange for L or g.
3. 3. Ignore bob mass for the ideal formula.
4. 4. Frequency f = 1/T after finding T.

Derivation

Small-angle SHM for a simple pendulum gives angular frequency ω = √(g/L):

1. Period T = 2π/ω:
   T = 2\pi\sqrt{\frac{L}{g}}
2. Solve for g (lab):
   g = \frac{4\pi^{2}L}{T^{2}}

Length L is to the center of the bob. Convert cm → m.

Examples

Example: L = 1 m, g = 10

T = 2π√0.1 ≈ 1.99 s.

Example: find L

T ≈ 2 s, g = 10 → L ≈ 1 m.

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