Pendulum Lab
Explore a small-angle pendulum with live motion and measurements.
Explore the lab
What you can explore
- Length and period
Change string length and gravity to compare the calculated ideal period with the motion.
- Angle and damping
Adjust initial angle and optional damping to inspect angular motion and decaying amplitude.
- Position and velocity
Show vectors and inspect the bob coordinates and velocity as the timeline advances.
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The model
Formula and underlying model
T = 2π√(L/g); θ(t) = θ₀ cos(√(g/L)t)- T
- Ideal oscillation period (s)
- L
- String length (m)
- g
- Gravitational acceleration (m/s²)
- θ, θ₀
- Current and initial angle; UI uses degrees (radians in formula)
- t
- Elapsed time (s)
Small-angle approximation; larger initial angles trigger a workspace warning. The displayed ideal period is independent of mass. The angle formula shown is undamped; optional damping modifies the motion.
The experiment
How it works
Define the pendulum
Set length, gravity and a small initial angle.
Play the motion
Advance or scrub time to inspect the bob and angular displacement.
Compare periods
Change length or gravity and compare ideal period, keeping damping off.
Learning outcomes
What you’ll learn
- Explain the square-root dependence of period on length.
- Recognize the limits of the small-angle model.
- Explain why mass does not affect ideal period.
Keep exploring
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Ready to experiment?
Explore Pendulum interactively
Open the lab, adjust the parameters, and see the results change in real time.