3A - Oscillations
10. Pendula
3A10.1 Simple Pendulum
A mass at the end of a string. (For dramatic effect, one could use the 50 lbs. pendulum of 1M40.1)
[Set-Up Time: 5 min.]
20. Springs and Oscillators
3A20.1 Mass on a Spring
A mass oscillates on a spring. A variety of springs and a set of different weights can also be provided.
[Set-Up Time: 5 min.]
Single Spring and Mass: 
Assorted Springs and Masses: 
3A20.2 Four Vibrating Masses
Show that the frequency depends on (k/m)^1/2. Four masses are held on separate flexible metal strips. The masses are: 1m, 1m, 4m, 4m; the strips are 1 k, 4k, 1 k, 4k. The first and last oscillators move at the same rate; the second one twice as fast, the third one twice as slow.
[Set-Up Time: 1 min.]
40. Simple Harmonic Motion
3A40.1 Circular Motion vs. Mass on a Spring
A mass moves up and down on a spring; a peg moves up and down on a rotating circle; a light source projects their shadows onto a screen, and the superimposed images move in synchronized motion.
[Set-Up Time: 15 min.]
Front View: 
Side View: 
3A40.52 Simple Harmonic Motion with a Pasco Motion Sensor
A Pasco motion sensor is used to record the motion of a mass oscillating on a spring or a pendulum. The output of the motion sensor is viewed in graphs of displacement, velocity and acceleration versus time on the computer; the image on the computer monitor can be projected onto a screen. The demonstration clearly shows the phase relationships between the position, velocity and acceleration and the effects of damping, if the oscillation is allowed to run for a minute or so.
60. Driven Mechanical Resonance
3A60.1 Tacoma Narrows Bridge Collapse - Video
Five to ten minutes of video showing the bridge before, during and after its collapse. From the Mechanical Universe series.
[Set-Up Time: 10 min.]
Side View: 
Front View: 
Back View: 
3A60.2 Forced Mechanical Oscillator
The frequency of a driving force on a spring can be varied to above, below, and (watch out!) at resonance. A mass hangs at the bottom of the spring, and it can be suspended in water to show the effect of damping. Warning: this apparatus is an antique.
[Set-Up Time: 15 min.]
70. Coupled Oscillators
3A70.1 Spring-Coupled Pendula
Two physical pendula are connected horizontally by a spring. Pull one pendulum back while holding the second one at equilibrium. Release, and the oscillation gradually transfers from the first pendulum to the second. Varying the height of the spring changes the period of the transfer.
[Set-Up Time: 15 min.]
3A70.10 Wilberforce pendulum
A mass with a large torsional moment hangs from a spring. Energy is transferred between vertical and torsional modes.
[Setup time: 2 min.]
75. Normal Modes
3A75.1 Spring-Coupled Pendula
Same as 3A70.1 above. This time, however, observe the two normal modes by a) releasing both pendula from the same side or b) releasing them from opposite sides.
[Set-Up Time: 15 min.]
3A75.10 Coupled harmonic oscillators (Normal modes)
Two or three riders on the air track are connected with springs to each other and to the air track frame. Normal modes can be excited by hand.
[Setup time: 15 mins.]
80. Lissajous Figures
3A80.1 Lissajous Figures on the Oscilloscope
Two function generators at different frequencies drive the horizontal and vertical inputs of an oscilloscope, projected on a TV screen.
[Set-Up Time: 20 min.]
95. Nonlinear Systems
3A95.45 Jump phenomena
A rider on the air track is driven sinusoidally but the restoring force (rubber bands) does not quite obey Hooke's law. This yields Duffing's equation rather than the familiar linear oscillator equation. The system exhibits jumps between high and low amplitude when crossing over the resonance.
[Setup time: 25 mins.]
3A95.60 Parametric resonance of a pendulum
The pivot of a pendulum is driven vertically at a variable rate. Driving at twice the pendulum's natural frequency excites the system into resonance.
[Setup time: 20 mins.]
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3B - Wave Motion
10. Transverse Pulses and Waves
3B10.1 Long Spring
Stretch a long spring across the front table. Give the spring a small pluck at one end and watch the pulse propagate down and back. Can show the dependence of wave velocity on tension by stretching the spring more or less.
[Set-Up Time: 2 min.]
3B10.2 Torsion Wave Machine (also called Shive or Bell Labs Wave Machine)
A long array of horizontal metal bars are fixed on a central wire. Pulling up on one of the bars at one end twists the spine and send a smooth wave down to the other end and back. Also shows standing waves (see Standing Waves 3B22.2).
[Set-Up Time: 5min.]
20. Longitudinal Pulses and Waves
3B20.1 Long Slinky
A long slinky is stretched across the table; compressing it suddenly sends a longitudinal pulse along it.
[Set-Up Time: none]
22. Standing Waves
3B22.1 Standing Waves on a String (formerly Modes of Vibration)
A long string is stretched across the full length of the front table; at one end it goes over a pulley to a mass hanging over the edge, at the other end it is driven by a mechanical oscillator. Vary the frequency of the oscillator using a function generator to show standing waves of different harmonics. The tension in the string can also be changed by adjusting the mass at the end of the string.
[Set-Up Time: 15 min.]
Images available soon.
3B22.2 Standing waves on the Torsion Wave Machine
Same apparatus as 3B10.2. Moving one end gently by hand, it is easy to set up a standing wave.
[Set-Up Time: 5 min.]
3B27.20 Columbia Wave Machine (Adding Waves Apparatus)
As a crank is turned, three sets of dots oscillate to show three types of wave motion: transverse, longitudinal, and composite (transverse + longitudinal, or "ocean" waves). This machine is an antique. The transverse dots are labeled "Ether Waves" - the patent for this apparatus was filed in 1905.
[Set-Up Time: 5 min.]
30. Wave Properties of Sound
3B30.1 Bell in a Vacuum
The sound of a ringing bell suspended inside a bell jar fades away as the air is pumped out.
[Set-Up Time: Unknown]
40. Doppler Effect
3B40.1 Doppler Whistle
Air is blown out the end of a long rotating pipe. As the speed increases, the pitch of the whistling rises and falls more dramatically.
[Set-Up Time: 20 min.]
50. Interference and Diffraction
3B50.1 Ripple Tank
A mechanical driver with two knobs sends ripples through water in shallow tank, and an overhead projector projects this image onto the screen. The relative phase and the frequency of the two knobs can be varied; in addition there is an assortment of one slit and two slit apertures as well as concave and convex reflectors that can be placed in the water.
Image Projected on Wall: 
3B50.22 Double Source Sound Interference
Two identical speakers are connected to an amplifier and a function generator. As students move around the room they clearly hear loud and soft spots as they walk along a row or move up and down. Measurements of distance can be made to determine the speed of sound.
[Note: This has only been tested in Rooms 428 and 329; it should also work in 301].
[Set-Up Time: 25 min]
3B50.40 Moire Transparencies
Transparencies with a circular wave pattern can be overlayed to show interference patterns.
[Setup time: 2 mins.]
3B50.52 Superposition Computer Simulation
This simulation program shows two differently colored waves approaching each other and the resulting superposition in a third color. Parameters which can be altered for each wave include wavelength, velocity, and amplitude. The image from the computer is displayed onto a TV screen.
[Set-Up Time: 15 min]
60. Beats
3B60.1 Beats with Tuning Forks
Two 256 Hz tuning forks are struck and shown to have the same pitch. Then a bit of clay is stuck to the side of one of the forks. Struck by itself, the difference is barely detectable, but a beat is heard if both forks are struck at the same time.
[Set-Up Time: 2 min.]
3B60.18 Beats with Function Generators
Two speakers are connected to different function generators. Beats can clearly be heard when the frequencies are nearly identical.
[Set-Up Time: 10 min]
Setup (except for additional function generator required): 
3B60.21 Beats Computer Simulation
Show beats using the program described in 3B50.52.
[Set-Up Time: 15 min.]
70. Coupled Resonators
3B70.1 Sympathetic Vibration in Tuning Forks
Two 256 Hz tuning forks are placed opposite each other. When one is struck, then stopped, the other can be heard (faintly - not ideal for a large lecture class!).
[Set-Up Time: 2 min.]
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3C - Acoustics
20. Pitch
3C20.1 Range of Hearing (or Limit of Audibility)
A series of metal bars with increasing frequencies up to 30 kHz. Strike them in order and discover that the students can hear more of them than you can. A similar effect can be accomplished using a function generator and varying the frequency from 10 kHz to 20 kHz.
[Set-Up Time: 2 min.]
50. Wave Analysis and Synthesis
3C50.1 Fourier Synthesis
A Fourier synthesizer connects to a speaker and oscilloscope, projected on TV screen. The synthesizer allows one to construct an arbitrary waveform by setting the amplitude and phase of a tone and its first nine harmonics.
[Set-Up Time: 30 min.]
3C50.13 Fourier Analysis of Sound
A sonometer computer program breaks up a sound (instrument, voice, tuning fork, etc.) into its Fourier components. The program shows the frequency of the harmonics on the y-axis as time scrolls through on the x-axis. The amplitude is displayed at the top of the screen in a graph showing the loudness of the sound on the y-axis as time scrolls through on the x-axis. The image from the computer is displayed onto a TV screen.
[Set-up Time: 20 min]
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3D - Instruments
30. Resonance Cavities
3D30.52 Resonance Fountain Tube
A horizontal meter-long tube filled with kerosene is driven by a speaker. At resonant frequencies the standing waves produce visible depressions at the antinodes, and large, erupting fountains at the nodes. The speaker is very loud upwards of 150 Hz.
[Set-Up Time: 15 Min.]
32. Air Column Instruments
3D32.1 Pipe Organ
A small wooden organ with a keyboard and interchangeable pipes can be connected to an external air supply.
[Set-Up Time: Unknown]
40. Resonance in Plates, Bars, and Solids
3D40.1 Musical Sticks
A set of wooden sticks will play a major scale when dropped on the table.
[Set-Up Time: 2 min.]
46. Tuning Forks
3D46.1 Tuning Fork Sets
Various sets of tuning forks in different scales.
[Set-Up Time: Unknown]
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