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  • G1-37: MASS ON SPRING WITH ULTRASONIC RANGER

    G1-37
    Plot graphs of position, velocity and acceleration for a mass oscillating on a spring.
    The ultrasonic range finder is used to plot graphs of position, velocity and acceleration for a mass oscillating vertically on a spring. Hanging masses with greater or lesser air resistance damping are available.
    Dr. Dan Russel of Penn State has developed some simulations of oscillating masses on springs that generate similar position graphs; compare the undamped and damped versions on his site.
    FS1, C2

  • G1-41: TORSIONAL PENDULUM - SMALL

    G1-41
    Demonstrate torsional SHM, and to show the effect of moment of inertia on the period.
    Various combinations of masses and moments of inertia can be placed on the platform to study the effect of changing the moment of inertia on the period of rotational SHM. This one is probably not adequate for quantitative measurements.
    G1

  • G1-42: TORSIONAL PENDULUM - LARGE

    G1-42
    Demonstrate torsional SHM and to show the effect of moment of inertia on the period.
    This large device executes torsional SHM on a heavy wire. Adding a cylindrical shell (hanging at top by wire support in photograph above) to the flat base increases the moment of inertia and very noticeably increases the period.

  • G1-43: KLINGER TORSIONAL VIBRATION MACHINE

    G1-43
    Demonstrate torsional SHM, and to quantitatively show the effect of moment of inertia on the period.
    Various combinations of masses and moments of inertia can be placed on the platform to study the effect of changing the moment of inertia on the period of rotational SHM. This one is adequate for quantitative measurements. Various available samples are showm in the photograph at the right.
    G1

  • G1-55: INERTIA BALANCE

    G1-55
    Illustrate the measurement of inertial mass using SHM.
    A mass is placed on the platform and set into motion, executing SHM horizontally. The period of the oscillation T = (1/2 pi) SQRT ((M+m)/k), where M is the mass of the platform and m is the unknown mass. Making period measurements with and without the unknown mass m one can determine its inertial mass.
    G1, ME1

  • G1-57: INVERTED PENDULUM - SPEAKER DRIVEN

    G1-57
    Demonstrate the conditions for stability of an inverted pendulum.
    A weighted straw hinged at the center of a loudspeaker is used as an inverted pendulum, which is driven by a sinusoidal wave to the speaker. The effect of variation of the driver frequency and amplitude on the stability can be easily studied.

  • G1-58: LOADED PENDULUM

    G1-58
    Analog to the longitudinal motion of a particle in a particle accelerator driven by a sinusoidal accelerating potential.
    The position of the pendulum bob, displaced from the vertical by the hanging weights, represents the phase of a particle being accelerated in a particle accelerator. The sinusoidal accelerating voltage creates oscillations of the particle about its equilibrium phase. The phase of the accelerating particle oscillates about the equilibrium phase, as does the pendulum.

  • G1-59: BIFILAR PENDULUM

    G1-59
    Illustrate a system with two pendular modes of oscillation.
    A ball is suspended by a string attached to another string which hangs from a support rod as shown in the photograph. In one direction the pendulum swings with a short length while in the orthogonal direction it swings with a much longer length. When the ball is moved in any other direction and released the resulting motion is a combination of these two orthogonal modes.

  • G1-71: LISSAJOUS FIGURES - SAND PENDULUM

    G1-71
    Demonstrate Lissajous figures.
    The bob is filled with sand, displaced from equilibrium and released or gently pushed. Its bifilar suspension causes it to execute Lissajous figures, which are traced out by the released sand.

  • G1-72: LISSAJOUS FIGURES - X-Y RECORDER

    G1-72
    Illustrate phase-changing Lissajous figures and to create Lissajous art.
    Using two oscillations below one Hertz with a few Volt amplitude, various neat Lissajous patterns can be obtained. For best results use frequencies very close to whole number frequency ratios.

  • G1-74: LISSAJOUS FIGURES - LASER AND LOUDSPEAKER

    G1-74
    Show Lissajous figures created by music to form a laser show.
    A front-surface mirror is suspended in front of the center of a large loudspeaker in an orthogonal suspension. A laser beam bounces off the mirror onto a nearby white screen, creating varying Lissajous patterns as the music plays. This suspension encourages the mirror to move with two basically orthogonal oscillations, combining to form Lissajous figures, as seen above.
    OS5

  • G2-02: FORCED HARMONIC MOTION WITH DAMPING - LARGE

    G2-02
    Demonstrate and graph driven and damped harmonic motion.
    Variable speed motor can be run below, at, or above the resonant frequency of a mass hanging on the spring. Two masses are provided. Inserting a felt-tipped pen into the holder and starting the paper rolling allows you to graph the motion of the oscillating mass.

    Note that this has been largely replaced by G2-09.

  • G2-03: RESONANCE IN TORSIONAL PENDULUM - PROJECTION

    G2-03
    Demonstrate quantitatively all aspects of the driven and damped oscillator.
    Using the "gross" and "fein" controls on the power supply box the frequency of the driving force can be swept through the natural frequency of the rotator. A knob on the power supply controls a damping magnet. Driven oscillations, under-damped, over-damped, and critically damped motion can be shown, and the maximum amplitude in the presence of various damping forces can be ascertained. A light source is optionally available for shadow projection.

    Practice before demonstrating this device. It is a very inclusive machine, and can be used to illustrate most aspects of damped and driven oscillations discussed in intermediate mechanics texts.

    Do not exceed the allowable damping voltage for more than a few seconds at a time, or the magnet may burn out.
    G2, ME2, LS1

  • G2-04: DAMPED OSCILLATIONS

    G2-04
    Demonstrate damped harmonic oscillations.
    Pull down or lift up the aluminum mass on the end of the spring and release to obtain oscillations. Moving the magnet so that the aluminum bar moves in the magnet gap creates very strong eddy current damping. By inserting a pen into the holder and scrolling the paper roll with the motorized drive, a graph of damped harmonic oscillation can be drawn.

    See G2-09 for the updated version of this demonstration.

  • G2-05: AIR TRACK - DRIVEN AND DAMPED OSCILLATIONS

    G2-05
    Illustrate the behavior of a driven and damped oscillator.
    A moveable glider, attached by stretched strings to a fixed glider at the left and an oscillator motor at the right, executes SHM when displaced and released. The oscillator can be driven by the variable frequency motor driver and damped by eddy currents by placing a magnet close to the base of the moving glider. The natural frequency of the glider can be changed by adding mass to the glider or by increasing the spring tension.

  • 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

  • G2-24: 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