Oscillations and waves
18 ready-made scenes and Python scripts. Each opens in the studio; press Play to run it, then change anything: masses, lengths, the forces, what the graphs show.
- Pendulum
A bob on a rigid rod, released from 38°. - Double Pendulum
Two rods, chaotic for almost any release angle. - Mass in a Slot Research
A mass in a slot with hatched channel walls, tied to the slot end by a spring (k, c). Labels, dimension x, frame I. - Pendulum on a Trolley Research
A pendulum hanging from a trolley that runs in a rail and is tied to its end by a spring. Angle arc θ, length ℓ, frame I. - Damped Oscillations Research
Three masses on springs, released alike: under-damped (ζ = 0.1) rings, critically damped (ζ = 1) returns fastest, over-damped (ζ = 2) creeps. - Coupled Oscillators Research
Two masses and three springs: pull one aside and the energy beats back and forth at the two normal-mode frequencies √(k/m) and √(3k/m). - Mass on a Vertical Spring Research
Released at the natural length, the mass falls 2mg/k: gravitational, elastic and kinetic energy trade places while the total stays constant. - Torsional Pendulum Research
A bar on a torsional spring (a pin with stiffness κ): T = 2π√(I/κ), whatever the starting angle. - Forced Oscillation near Resonance Research
A force F₀ sin 2πft drives a damped mass-spring near its resonance (f₀ = 0.95 Hz). Change f or F₀ in Data → Constants and run again. - Shake Table Research
The table moves x = A sin 2πft. A block slips when the table's acceleration A ω² passes μ_s g: the least grippy slips first. - Rod and Point Mass: the Parallel-Axis Theorem Research
A pinned bar and a bob of the same mass and length, released from 8°: the bar's mass is spread out, I = mL²/3, so its period is √(2/3) times the bob's. - Pendulum Wave Research
Fifteen pendulums of slightly different lengths drift out of step into waves, two groups, three, and line up again after exactly 60 s. - Cars over Bumps: Suspension Research
Two cars on springs drive over the same bumps. Weak dampers (ζ = 0.1) keep bouncing; ζ = 0.6 settles after one swing. - Pendulum period against amplitude Python Research
Release a pendulum from 5° to 150°: the period against 2π√(L/g) and the exact value. - Resonance curve of a driven oscillator Python Research
Step the driving frequency up and measure the amplitude: the resonance curve against theory. - A pulse along a chain of springs Python Research
Strike one end of a chain of 30 masses: the pulse travels at a√(k/m). - Chaos: two nearly identical double pendulums Python Research
A difference of 10⁻⁴ rad grows until the two motions are unrelated. - Measure g with pendulums (a least-squares fit) Python Research
Six pendulums from 0.25 to 2 m are timed; a straight-line fit of T² against L gives g = 4π²/slope.