Simple Pendulum
A rigid simple pendulum with adjustable length, gravity, and damping. Compare small-angle harmonic motion with larger amplitudes where the period depends on amplitude.
Who it's for: Waves and mechanics courses; demos of periodic motion and damping.
Key terms
- pendulum
- period
- small-angle approximation
- angular frequency
- damping
Live graphs
How it works
A simple pendulum obeys nonlinear equation θ¨ + (g/L)sinθ = 0. For small angles, sinθ ≈ θ and the motion is simple harmonic with period T ≈ 2π√(L/g). Larger angles increase the period. Damping removes energy over time.
Key equations
More from Classical Mechanics
Other simulators in this category — or see all 63.
Conical Pendulum
Steady cone: ω(θ,L), T and mg vectors, T_rev vs simple-pendulum T₀.
Physical Pendulum (Rod)
Thin uniform rod: pivot along L, I and T(δ), equivalent length L_eq.
Pendulum Collision
Two bobs: hit along normal, e elastic; θ¨ between hits vs 1D collisions.
Yo-Yo Dynamics
Unwinding string: a = g/(1+I/mr²), T, α, optional friction torque τ.
Satellite Yo-Yo Despin
L = const: ω_f = ω_0(I+2mr_i²)/(I+2mL²) as tethers pay out from r_i to L.
Rubber Sheet & Ball
Sheet height ∝ −Σm/r; ball rolls along −∇h — embedding metaphor, not GR.