Oscillations Topic

Pendula

Concept 5 demos

Yellow chalk-line bob swinging on a short string from a horizontal rod on a clamp stand, with motion blur showing a wide arc in front of a chalkboard

Simple Pendulum

A simple pendulum with easily adjustable string length demonstrates how period depends on length:. The bright yellow bob is visible even in the largest lecture halls.

Ring stand with horizontal rod supporting multiple pendulums of different lengths and bob types (cork cylinder, golf ball, plumb bob, green ball) on white and red strings

Pendulum Experiments

A do-it-yourself pendulum kit for investigating period dependence on length , independence from mass, and the small-angle approximation. Assemble pendulums to match clicker questions or run in-class experiments.

Two pendulums hanging from a horizontal rod between two tall bench clamp stands, with black nylon string looped over ring clamp hooks and brass mass hangers at the bottom; a blue PASCO mass set sits on the bench

Twin Pendulums

Demonstrates that the period of a simple pendulum is independent of mass. Two pendulums of equal length but different masses remain synchronized over many swings, directly testing and challenging the …

Springs and Oscillators

Concept 1 demo

Bench clamp stand with horizontal rod supporting two flat spring strips hanging from hooks, each with a brass cylindrical mass attached. Additional masses sit on the green bench surface.

Mass on a Spring

Demonstrates Hooke's Law and simple harmonic motion. Hang different masses from springs to show the linear force-displacement relationship and that the period of oscillation depends on mass:.

Simple Harmonic Motion

Concept 2 demos

Motor on wooden block with white ball on rotating shaft, spring-mass system hanging from horizontal rod between bench clamp stands, fiber optic lamp at left, blue Radiotrol speed control box in front, white backdrop behind

Linear and Rotating Motion

A motorized rotating ball is synchronized with a mass-spring oscillator to show that SHM is the projection of uniform circular motion. A lamp casts shadows of both onto a backdrop, …

Angular acceleration machine with aluminum disc and metal arm mounted on a wooden block, secured to table with Irwin Quick-Grip clamps; a string from the axle suspends a brass mass

Asymmetric Oscillator

Demonstrates coupled rotational and translational motion in an asymmetric system. Students observe how removing one mass from the angular acceleration machine creates two unstable equilibrium positions at different potential energies, …

Driven Mechanical Resonance

Concept 4 demos

Black bowling ball suspended by cable and hardware, with a hand giving it a gentle push; white floor and yellow wall visible in background

Resonant Bowling Ball Pendulum

A bowling ball on a 5.4 m cable forms a pendulum with a ~4.7 s period. Gentle pushes on alternating sides every ~2.3 s (matching the half-period) build large-amplitude swings …

Flexible metal strip loop mounted vertically on a clear cylindrical base with driver mechanism, connected to a Daedalon audio driver box displaying 22.3 Hz. The loop is visibly distorted into a non-circular shape by the 3rd harmonic standing wave.

Resonance in a Loop

Demonstrates resonance and harmonics of standing waves on a vibrating loop. Students observe that only specific discrete frequencies produce stable standing wave patterns, illustrating boundary conditions and wavelength quantization in …

Seven dark blue metal leaf springs of decreasing height with brass block caps, mounted on a brass rail on a red wooden base, with motor and pulley assembly at right end

Leaf Springs Resonance

As the motor speed scans from low to high frequency, successively shorter leaf springs resonate one by one, oscillating violently when the driving frequency matches their natural frequency. Students see …

Coupled Oscillations

Concept 4 demos

Wilberforce pendulum: long helical spring suspended from a rod and clamp system, with a cylindrical brass bob at the bottom fitted with a horizontal cross-bar carrying adjustable masses

Wilberforce Pendulum

Demonstrates coupled oscillations and energy transfer between two modes of vibration. Students observe energy periodically transferring between vertical bouncing and torsional twisting when the mode frequencies are matched.

Long-exposure photo of the spring-mass system in motion, showing a complex blur pattern as the masses oscillate in both vertical and horizontal modes simultaneously

Autoparametric Resonance

A spring-mass system spontaneously transfers energy between vertical bouncing and pendulum swinging modes through autoparametric resonance. Demonstrates parametric excitation, mode coupling, and the 2:1 frequency condition for energy transfer between …

Front view: five metronomes in a row on a white foam board balanced on two soda cans inside a clear plastic tank

Coupled Metronomes

Five metronomes set to the same tempo start out of phase on a movable platform. Within about a minute, weak mechanical coupling through the platform causes them to synchronize spontaneously. …

Normal Modes

Concept 1 demo

Two PASCO dynamics carts on an aluminum track connected in series by three springs between the track bumpers

Oscillating Carts

Demonstrates normal modes of coupled oscillators. Students observe in-phase and out-of-phase motions, beat phenomena from mixed initial conditions, and how the number of normal modes scales with the number of …

Lissajous Figures

Concept 1 demo

Agilent dual-channel function generator (left) and Agilent InfiniiVision digital oscilloscope (right) displaying a blue Lissajous figure in XY mode, connected by two BNC cables

Lissajous Figures

Displays Lissajous figures on an oscilloscope in XY mode to show how frequency ratios and phase differences between two sinusoidal signals produce characteristic closed-curve patterns. Students learn to read frequency …

Non-Linear Systems

Concept 2 demos

Double pendulum in motion: a red vertical support bar topped by a black pivot bracket, with a blurred silver bar swinging through a wide arc. The base is clamped to the table with blue and yellow clamps.

Chaotic Double Pendulum

Demonstrates chaotic motion and sensitive dependence on initial conditions in a simple two-degree-of-freedom system. At low energy the pendulum shows predictable coupled oscillations; at higher energy it transitions to chaotic, …

Wooden frame with a dowel rod suspended by a swivel chain from a horizontal crossbar. A ceramic ring magnet is attached to the bottom of the dowel. Below, a gray metal base plate holds three ring magnets arranged in a triangle pattern.

Magnetic Pendulum

Demonstrates chaotic motion and sensitive dependence on initial conditions using a magnetic pendulum over configurable base magnets. Students observe how small changes in release position lead to capture by different …