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Oscillations

  • G2-07: PSYCHOACOUSTIC VIBRATION TRANSDUCER

    G2-07
    Challenge your students to recognize pseudoscience while illustrating resonance
    A traditional explanation: "When a group of people concentrate on one of the pendula, held as shown by the instructor, their psychoacoustic brain waves rapidly become in phase, producing enough mechanical energy to make only that pendulum oscillate."

    Of course, this is actually a demonstration of driven resonance - with a bit of practice, via small movements of your hands you can drive any one of the pendula you choose. Encourage your students to analyze pseudoscientific explanations for real phenomena.
    G2

  • G2-09: FORCED HARMONIC MOTION WITH SONAR

    G2-09
    Plot a graph of forced damped harmonic motion near the resonant frequency.
    A computer and ultrasonic range finder is used to plot the motion of a large mass on a spring driven near its resonant frequency. With a large amount of damping, the result is a change in the amplitude of the oscillation, as shown in the photograph above.
    FS1, C2

    g2-09a

  • G2-11: RESONANT SAW BLADES - HAND DRIVEN

    G2-11
    Show that a mechanical oscillator responds with a maximum amplitude to its own resonant frequency.
    Three saw blades of different lengths have been rigidly attached to a manual shaker. Shaking the assembly, one can find the resonant frequency of each saw blade.

    For a similar power-driven demonstration, see G3-45.
    G2

  • G2-12: BARTON'S PENDULUMS

    G2-12
    Demonstrate driven resonance.
    A set of non-coupled pendula are placed on a platform that rocks at the same frequency as one of the center pendula. The rocking motion drives the motion of the pendulum with which it is resonant, but only partially drives the others, showing systematically how a vibrating system responds when the natural frequency is below, at, and above the driving frequency, as seen in the photograph at the right.

    g2-12a

  • G2-21 COUPLED PENDULA

    G2-21
    Demonstrates coupling of motion between two pendula of the same length
    The pendula are hung from a rod which can rock back and forth to transfer the motion from one pendulum to another. If you start the pendulum at the left in motion (in and out of the picture), the motion will couple back and forth between the pendula of the same length, leaving the others with only a slight perturbation. It is of interest to note the phase of the two pendula as the motion is transferred back and forth.

    Invite a student up to measure the pendula to confirm that the responsive one matches in length.

  • G2-22: BAR-COUPLED PENDULA

    G2-22
    Demonstrate a coupling resonance and to show normal modes.
    By starting either pendulum in motion in the plane of the picture, one observes transfer of the motion between the two pendula. One can also produce the two normal modes: both pendula moving in phase, or the pendula moving out of phase.
    FS2

  • G2-23: SPRING-COUPLED PHYSICAL PENDULA

    G2-23
    Demonstrate resonance and normal modes.
    After starting one of the pendula into motion in the plane of the picture, the motion couples back and forth between the two physical pendula at a rate determined by the spring constant and its location. Coupling can be varied by sliding the spring clamps along the pendula shafts. Normal modes can be nicely demonstrated.
    FS2

  • G2-24: COUPLED PENDULA - 100 TO 1 MASS RATIO

    G2-24
    Illustrate mechanical resonance.
    The two pendula have the same length, but the mass of the upper bob is 100 times that of the lower bob. With the masses hanging motionless, gently tap the bigger mass. Its energy will couple to the smaller mass, causing the smaller mass to oscillate with a much larger amplitude. The energy then couples back to the larger mass, and the cycle repeats.

  • G2-25: COUPLED PENDULA - 1000:100:10:1 MASS RATIO.

    G2-25
    Illustrate a complex resonance system.
    Four pendula are suspended in series from a pole. Each have the same length; the largest is 5000 g and the smallest 5 g. The supporting pole must be securely clamped to the table. Invite students to predict how a movement of the uppermost weight will affect the others.

    Tap the heaviest (top) weight gently. Energy couples downward through the pendula, with the amplitude of each successive pendulum becoming greater.

    This demonstration is an analog to the system developed by University of Maryland Physics Professor J. P. Richard to increase the amplitude of the vibration from gravitational wave antennas. The mechanical vibration is then converted into an electrical signal using a transducer.
    G2, FS1

  • G2-26: COUPLED AIR TRACK GLIDERS

    G2-26
    Demonstrate coupled oscillations and normal modes in a system of two identical coupled air track gliders.
    Two moveable air track gliders are connected by three springs to fixed gliders (at each end). Pushing one of the gliders causes motion which rapidly couples back and forth between the two gliders. The two normal modes can be excited by giving the two gliders the same displacements, either (1) in phase, or (2) out of phase, before releasing them from rest simultaneously.
    FS2

  • G2-27: COUPLED SERIES MASSES HANGING ON SPRINGS

    G2-27
    Illustrate coupled oscillations and normal modes.
    Pushing either mass causes oscillations which will couple between the two masses. If the two masses are displaced from equilibrium by the appropriate amount either (1) in phase, or (2) out of phase, the normal modes can be produced. Alternatively, moving your hand up and down at the frequency of a normal mode will excite that mode.

    Check out Erik Neumann's Double Spring simulation here!
    G2

    g2 27edit

  • G2-28: COUPLED PENDULA WITH VARIABLE DRIVER

    G2-28
    Show that the maximum coupling occurs between pendula of the same length.
    Adjust the length of the driver pendulum, on the left, so that it will couple to either of the other two. Coupling occurs through movement in the frame.
    FS2

    g2-28a

  • G2-41: WILBERFORCE PENDULUM

    G2-41
    Demonstrate a linear coupling resonance and normal modes.
    Move the bob straight up or down a few inches and release it quickly. It first starts to oscillate vertically, then its energy transfers entirely into rotational motion, then back to pure translation. This motion then repeats. By lifting the mass directly upward and at the same time rotating it (in either direction) before release, the two normal modes of the Wilberforce pendulum can be produced.

    g2-41a

  • G2-42: ELASTIC PENDULUM

    G2-42
    Demonstrate a non-linear coupling resonance and stable fixed points.
    Start the spring oscillating vertically; the energy will then couple back and forth between pendular motion and vertical spring motion. Stationary combinations of these two oscillations (corresponding to normal modes in a linear resonance) can also be produced, by pulling the weight simultaneously down and to the side. Adding an additional weight (attached to the support shaft near the bottom of the picture) to the spring destroys the resonance, resulting in less than total transfer of energy between the pendulum and spring motion.

    This non-linear coupling resonance occurs when the spring (vertical) frequency is twice the frequency of a pendulum of the length at equilibrium. This is of interest because it is a very good mechanical analog to the v(r) = 2 v(z) resonance in the extraction region of a sector-focused cyclotron, where v(r) and v(z) are the radial and vertical betatron frequencies.

    The mass required to be connected to a spring to induce this behavior can be determined as follows by noting the resonant condition:

    v(mass on spring) = 2 v(pendulum)

    or

    sqrt[ k/m ] = 2 sqrt[ g/L ]

    so

    k = 4 mg/L

    This means that you must add a weight so that the increase in length of the original spring is 1/3 of the original spring, or 1/4 of the length of the final spring (spring constant = mg/[L/4]).

  • G3-11: SHIVE WAVE MACHINE - RESONANCE ABSORPTION

    G3-11
    Demonstrate resonance absorption of wave energy by a mass-on-spring system.
    Sending a wave along the machine drives the spring-mass attached to one of the crossarms. The greatest effect will be at the resonant frequency for the mass on the spring. A well chosen driving frequency will result in almost complete absorption of the wave.

  • G3-41: WAVE MODELS - PROJECTION

    G3-41
    Demonstrate standing waves, travelling waves, and superposition of waves.
    The wave models are projected and individual members rotated to show particular wave characteristics. Models are: (1) identical waves moving in opposite directions, (2) sum of waves in (1), (3) traveling wave and same with twice the amplitude, (4) identical waves 90 degrees out of phase and their sum, (5) identical waves 180 degrees out of phase.
    G3

  • G3-45: RESONANCE OF WIRES

    G3-45
    Show standing waves in heavy wires fixed at one end.
    This uses the mechanical oscillator from G3-46 attached to a trio of wires similar to demonstration G2-11. As the frequency of the oscillator is increased, standing waves appear in each successively shorter wire.
    G3

  • G3-46: STANDING WAVES IN A WIRE LOOP

    G3-46
    Illustrate circular standing waves; to use as a model of stationary states in atoms corresponding to standing waves of electrons in Bohr orbits.
    A wire loop is attached to a mechanical vibrator (the same as used in G3-45). Regulating the frequency of the motor produces different standing wave configurations of the wire loop.
    G3

  • G4-11: SOAP FILM OSCILLATIONS

    G4-11
    Demonstrate standing waves in a two-dimensional medium.

    A large rectangular frame or a circular frame (from M4) are provided for producing soap films using a specially-formulated soap solution. Careful movement allows production of various standing waves.

    Please specify in comments when ordering if you want the circular form, square form, or both.
    OS2, M4

  • H1-27: SPEED OF SOUND - LISSAJOUS FIGURES

    H1-27
    Measurement of the speed of sound in air using Lissajous figures.
    The signal to the loudspeaker is used as the horizontal input of an oscilloscope, and the signal picked up by the microphone is used as the vertical input, forming Lissajous figures. When they are in phase a diagonal line is produced, running from the lower left to the upper right of the oscilloscope screen. This situation is seen in the photograph above.

    As the microphone is moved away from the loudspeaker the vertical signal falls 90 degrees behind in phase, causing the Lissajous figure to form an ellipse. When the two signals are out of phase (180 degrees phase difference) the pattern is a line along the opposite diagonal. As the microphone is withdrawn further, the microphone signal becomes 270 degrees behind in phase and the pattern again becomes an ellipse. One important difference between the two ellipses is that they are rotating in opposite directions, but this is not observable on the oscilloscope. Withdrawal of one full wavelength, when the signal from the microphone lags a full period (360 degrees) behind the original condition, creates a pattern similar to the original pattern. In this case the signal picked up by the microphone is reduced in amplitude due to the inverse square law, reducing the slope of the line.

    For the most accurate measurement a frequency meter is connected to the trigger output of the oscillator. In the case shown below:

    S = 3385Hz x 104mm = 352 m/s.

    The photographs above show the Lissajous patterns at 90 degree intervals as the microphone is withdrawn.