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Oscillations

  • A1-21: METRONOME

    A1-21
    Means to show different intervals of time
    A typical mechanical metronome, beats between 40 and 208 clicks per minute. Useful for introducing the concept of time measurement.

    Invite students to speculate about the mechanism of changing the time base - why does moving a weight change the rate? This can be related to concepts of levers, moment of inertia, and mechanical harmonic oscillators.
    A1

  • B4-01 HOOKE'S LAW

    B4-01
    Demonstrate the linear relationship between force and stretching for a simple spring.
    Two weights are provided to show linearity over a factor of two in applied force.
    FS2

  • B4-02: HOOKE'S LAW - COMPRESSING A SPRING

    B4-02
    Demonstrate Hooke's law for a spring under compression.

    This tabletop demonstrations illustrates Hooke's Law in compression, for comparison to the typical hanging-spring examples. Add weights to observe that the compression of the spring is approximately proportional to the amount of weight added.
    FS2

  • C1-11: AIR TRACK - CENTER OF MASS PENDULUM

    C1-11
    Show uniform motion of the center of mass of a vibrating pendulum/glider system.
    A symmetric (balanced) pendulum is suspended from an air track glider. The mass of the pendulum bob is approximately the same as that of the glider, so the center of mass (marked by a fluorescent disc) is approximately at the midpoint of the rod between the bob and the center of the glider. When the pendulum oscillates, the center of mass moves uniformly in the horizontal direction or remains motionless (horizontally).

  • C1-12: AIR TRACK - CENTER OF MASS OF COUPLED GLIDERS

    C1-12
    Demonstrate uniform motion of the center of mass of an oscillating system.
    As the gliders oscillate while moving along the air track, the center of mass (marked by an orange dot on the spring) moves with a constant velocity.

  • C1-13: AIR TRACK - REDUCED MASS

    C1-13
    Demonstrate the change in frequency for two-body oscillations.
    Two gliders are connected by a steel spring as shown in the photograph. With one mass taped down, the other mass vibrates with the standard period for simple harmonic motion: T = 2 pi sqrt (m/k), where k is the spring constant and m is the mass of the vibrating glider. If the two masses are pulled apart and released simultaneously, they vibrate out of phase with each other about the center of mass with a period T = 2 pi sqrt (u/k), where u = Mm/(M+m) is the reduced mass of the system. For M=m the reduced mass u = m/2, and the period is less by a factor of sqrt(2) = 1.414 than in the case of one glider oscillating.

  • C8-03: GALILEO'S PENDULUM

    C8-03
    Demonstrate conservation of energy in a simple system.
    The pendulum is hung from the upper peg with the lower peg interrupting its swing to the right. When started from the left at a given height, the pendulum rises to that same height on the right, after being stopped by the lower peg.

    See demonstration G1-20 to explore more complexities of this setup.
    FS2

  • D1-63: MAXWELL PENDULUM - LARGE

    D1-63
    Demonstrate transformations between gravitational potential energy and rotational kinetic energy.
    Used as a large-scale yo-yo, transformation of energy can easily be observed by a large class. Wind the string around the small spool radius, hold with the axis horizontal, and release. The initial gravitational potential energy is converted primarily into rotational kinetic energy, with a lesser amount of translational kinetic energy, as the device moves downward, with conversion back to gravitational potential energy after the spool reaches its minimum position and moves back upward.

  • D1-64: MAXWELL PENDULUM - SMALL

    D1-64
    Demonstrate transformations between gravitational potential energy and rotational kinetic energy.
    Wind the string up on the small axel, giving the device some initial gravitational potential energy. When released, this gravitational potential energy is converted into rotational kinetic energy, with a lesser amount of translational kinetic energy, as the device moves downward, then converted back as it rises. Two different sizes of small axels are available.

  • D1-65: YO-YO

    D1-65
    Illustrate transformation between various forms of energy and to perform yo-yo tricks.
    Simply holding the end of the string to allow the yo-yo to unwind and wind back up again illustrates transformation between gravitational potential energy and rotational kinetic energy, with a lesser amount of translational kinetic energy. See Demonstration Reference File for further information on yo-yo tricks.

  • D2-13: RACING PENDULA

    D2-13
    Illustrate in a counter-intuitive way the effect of moment of inertia on rotational acceleration.

    Two physical pendula, one of which has a weight on its bottom end, are held in a horizontal position and released from rest simultaneously. Q: Which one will reach the bottom first, or will it be a tie. A: The one without the weight will accelerate faster and reach the bottom first. This can be a rather tricky question, requiring careful analysis by the student. Mislead them by pointing out that pendula of the same length have the same period!

    In this apparatus the position of the weight can be adjusted and set using a thumbscrew. Q: Where must the bob be placed so that the two pendula will accelerate at the same rate and reach the bottom simultaneously? A: At one-third of the distance from the bottom end. The period of a physical pendulum is equal to that of a simple pendulum with two-thirds of the length of the physical pendulum.
    FS2

    d2 13

  • D2-42: MOMENT OF INERTIA -TORSIONAL CHAIR AND BOARD

    D2-42
    Demonstrate moment of inertia using the torsional chair.
    The chair can be assembled with a large spring (under the seat) connected such that the chair executes simple harmonic motion about an equilibrium position. The period of oscillation depends on the moment of inertia of the chair plus the moment of inertia of anything else attached to the chair. The period of oscillation can be measured without and with the board clamped to the chair. Other weight can be added, and is available on request.

  • D2-43: MOMENT OF INERTIA - TORSIONAL CHAIR AND WEIGHTS

    D2-43
    Demonstrate the effect of moment of inertia.
    A spring is connected beneath the chair so that when started into motion it executes simple harmonic motion about some equilibrium point. A subject sitting on the chair holding the weights can vary the moment of inertia by holding the weights in or holding the weights out by extending his or her arms. The further out the weights are held, the greater the moment of inertia, and thus the more slowly the chair (plus occupant) oscillates.
    FS0

  • D2-51: BICYCLE WHEEL PENDULUM

    D2-51
    Demonstrate the Parallel Axis Theorem.
    A bicycle wheel is suspended at its axis on a physical pendulum, as seen in the photograph above. Set it swinging, and invite students to predict how its motion will change if the wheel is given some initial rotation versus with it initially not rotating versus with it fixed and unable to rotate (cord for fixing wheel available upon request).

    This demonstration can be used to introduce the Parallel Axis Theorem.

  • D3-12: SWING MODEL

    D3-12
    Model the pumping of a swing using conservation of angular momentum.

    A mass (the swing) hangs from a rope that passes over a pulley and is connected to the support post. A second shorter rope hangs freely from the horizontal section of the main rope.

    Start the pendulum mass oscillating with a small amplitude. When the pendulum gets to its lowest position, pull gently down on the shorter rope, shortening the pendulum and thereby increasing its velocity. Release the rope as the pendulum nears its high point.

    According to a possibly oversimplified analysis, conservation of angular momentum at the low point, before and after the pull is applied, explains why this procedure causes the amplitude of the swing to increase with time. See also discussion of parametric resonance.
    D3, FS2

  • D3-32: KEYWHIP

    D3-32
    Demonstrate angular momentum conservation in a surprising way.

    A string about one meter long has a (relatively heavy) set of keys on one end and a (very light) match box on the other end. The string passes over a pencil with the keys hanging down and the matchbox held horizontal to the pencil with about two/thirds of the string between the pencil and the matchbox.

    Q: What will happen when the match box is released?

    A: Surprisingly, the keys will not fall to the floor. When the matchbox falls it develops angular momentum. Conservation of angular momentum of the matchbox causes it to rotate very rapidly about the pencil as the string pulls it in. Before the string is used up, the matchbox string actually wraps around the pencil, preventing the keys from falling onto the floor!

  • D5-13: FOCAULT PENDULUM - MODEL

    D5-13
    Model the Foucault pendulum
    The circular base can be rotated while the pendulum oscillates in a fixed plane in the frame of reference of the laboratory, thus showing the apparent rotation of the plane of the pendulum when viewed in the frame of reference of its base.
    D5, OS10

  • D5-22: ROTATING PENDULUM

    D5-22
    Demonstrate the presence of a "critical parameter" which determines the dynamic behavior of a simple physical system.
    Attach a mounting frame to a variable speed rotator with the length of the pendulum of 10 cm. Adjust the rotation rate to less than about 1.6 revolutions per second, and the bob will remain in stable equilibrium in the vertical position. For rotational rates greater than 1.6 revolutions per second, the stable equilibrium position of the bob will be non-zero, depending on the rotation rate. For angular speeds greater than 2 or 3 revolutions per second the pendulum is erratic. For angular speeds less than about 3 revolutions per second the presence of a non-zero stable equilibrium position is readily demonstrated. Adjusting the length of the pendulum will change the critical angular speed.
    D5, D1

  • D5-24: ROTATING PENDULA - LENGTH VS. HEIGHT

    D5-24
    Show that pendula of different length suspended from the same point rotating at the same angular speed rise to the same vertical height.
    When the device is rotated at an angular speed w the angle a from the vertical which a pendulum of length l will assume is given by cos a = g / w^2 l, where g is the acceleration of gravity. The vertical distance of each from the support point is l cos a = g / w^2, the same value for each of the pendulum. This can be easily observed using the apparatus.

  • F2-22: BUOYANCY PARADOX - ACCELERATED FRAME

    F2-22
    Illustrate dramatically the concept of buoyancy.
    A float is at rest in a water vessel suspended by a spring from a fixed point. The vessel is lifted up and released from rest, so that it oscillates vertically on the spring. In the picture above a band around the floater lies between the two bands around the larger vessel when the system is at rest.

    Q: How will the float move inside the water vessel as the vessel executes simple harmonic motion?

    A: Surprisingly, the float will remain at rest in the water vessel as it oscillates. It will even remain at rest when the vessel is stopped suddenly with your hand! See video 2 below. As the vessel oscillates, the weight density of both the floater and the water bath vary together, as the acceleration of the vessel varies, so the ratio of their densities remains the same, and they will continue to float with the same geometrical relationship!!