Pendulum Period Calculator
Calculate a simple pendulum’s period and frequency with a large-amplitude correction.
Step-by-step working
- T₀ = 2π√(L/g) = 2π√(1/9.80665) = 2.0064 s
- θ₀ = 10° → T ≈ T₀(1 + θ²/16 + 11θ⁴/3072) = 2.0102 s
Mathematical Formula
Overview & Explanation
A pendulum’s period depends on length and gravity; larger swings take slightly longer.
How It Works
- Compute the small-angle period.
- Apply the series correction for amplitude.
Practical Applications
- Clock design.
- Measuring g in labs.
Example 1: 1 m at 10°
≈ 2.01 s.
Inputs
Length (m): 1 · Amplitude (°): 10 · Gravity (body): Earth (9.80665 m/s²)
Step 1
T₀ = 2π√(L/g) = 2π√(1/9.80665) = 2.0064 s
Step 2
θ₀ = 10° → T ≈ T₀(1 + θ²/16 + 11θ⁴/3072) = 2.0102 s
Period (amplitude-corrected)
Result
Example 2: 0.25 m at 45°
Large swing.
Inputs
Length (m): 0.25 · Amplitude (°): 45 · Gravity (body): Earth (9.80665 m/s²)
Step 1
T₀ = 2π√(L/g) = 2π√(0.25/9.80665) = 1.0032 s
Step 2
θ₀ = 45° → T ≈ T₀(1 + θ²/16 + 11θ⁴/3072) = 1.0432 s
Period (amplitude-corrected)
Result
How it's calculated & sources
T₀ = 2π√(L/g); T ≈ T₀(1 + θ₀²/16 + 11θ₀⁴/3072) for amplitude θ₀ in radians.
Frequently Asked Questions
Does mass matter?
Seconds pendulum?
How accurate is the correction?
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