SHM & MOMENTUM CONSERVATION — INTERACTIVE MODEL

Newton's Cradle
a coupled pendulum system

Five identical steel spheres, each a rigid pendulum θ̈ = −(g/L)sin θ − cθ̇, coupled by near‑elastic contact collisions e ≈ 1. Pull a sphere and release it — momentum and kinetic energy propagate through the chain in accordance with conservation law.

Live State ● running

Angle θ
0.00rad
Ang. velocity ω
0.00rad/s
Kinetic energy
0.00J
Potential energy
0.00J
Total mechanical energy (system)
0.00J
Period (measured)
—s
Period (theory 2π√(L/g))
0.00s
Collisions
0
Sim time
0.00s

Phase Portrait sphere 5 · (θ, ω)

trajectorycurrent state

Energy Budget KE / PE / total

kinetic potential total

Parameters

9.80 m/s²
4.00 m
0.995
0.010
1

Controls

Drag a sphere to pull it back, release the mouse to let go.
Drag empty space to orbit the camera · scroll to zoom.
Model rendered client‑side · symplectic (semi‑implicit Euler) integrator, 6 substeps/frame