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Oscillations

  • F2-24: ACCELERATED BUOYANT BALL

    F2-24
    Illustrate buoyancy in a paradoxical way.
    A ping pong ball is tethered by a spring to the bottom of a water container, which in turn hangs from a spring attached to a fixed point. At rest, the ping pong ball floats near the center of the water tank. Q: How does the ping pong ball move, if at all, when the water tank is raised vertically and released from rest, so that it executes simple harmonic motion? A: The ping pong ball moves out of phase with the motion of the water tank. The system functions as an accelerometer, where the ball moves (with respect to its equilibrium position) in the direction of the acceleration of the tank. The magnitude of the displacement is roughly proportional to the magnitude of the acceleration of the tank.

    f2-24a

  • F4-23: WATER PENDULUM

    F4-23
    Show the surface of a container of water in a swinging pendulum.
    A container with water is suspended as a pendulum. When the container is held to one side, the water moves to its lowest point and the surface remains horizontal. When it is released and swings as a pendulum, the water spreads out uniformly on the bottom of the container and stays at rest at all times.
    F4, F1, FS1

  • G1-11 COMPARISON OF SHM AND UCM

    G1-11
    Demonstrates the relationship between simple harmonic motion and uniform circular motion.
    Turning a crank on the rear of the apparatus causes the center ball to move in circular motion around a 30cm diameter orbit, while the ball on top executes simple harmonic motion. It can be seen that SHM is the projection of UCM. This device can also be used to discuss the concept of degrees of motion in SHM by comparison with the reference circle.

  • G1-12: PENDULUM AND ROTATING BALL

    G1-12
    Demonstrate that simple harmonic motion is the projection of uniform circular motion.
    A ball rotates on a phonograph turntable below a physical pendulum with a ball on its end. The device is shadow projected on a white screen using a bright point light source. The pendulum is set to the same period as the turntable, so when the pendulum is started in the correct phase, the projection of the rotating ball moves along with the projection of the pendulum.
    FS2

  • G1-13: MASS ON STRING

    G1-13
    Illustrate uniform circular motion.
    Rotate the mass on the string, creating uniform circular motion. This is helpful in the context of discussion of SHM and the relationship between SHM and UCM.

    In carefully controlled spaces, consider asking students what path the rotating mass would take if you released the string. (Please do not hit the students.)
    G1

  • G1-14 PENDULA WITH DIFFERENT MASSES

    G1-14
    Demonstrates independence of a simple pendulum's period with mass of the bob.
    Four geometrically identical pendula have bobs made from lead, brass, stainless steel, and aluminum, respectively. Their periods are the same.
    FS2

  • G1-15 PENDULA WITH 4 TO 1 LENGTH RATIO

    G1-15
    Shows that period of a simple pendulum is proportional to the square root of its length
    The two pendula are started in phase. The shorter pendulum undergoes two complete oscillations for each oscillation of the longer pendulum.
    FS2

  • G1-16: PENDULUM WITH LARGE OSCILLATION

    G1-16
    Show the difference between pendula with small amplitude and large amplitude of oscillation, and to show rotational motion where the kinetic energy at the top is much less than the change of potential energy from the top to the bottom of the oscillation.
    The Oberbeck Cross is used with three of the weights at their minimum and one at its maximum radius. The motion of the pendulum for various amplitudes, including complete rotation, can be simply observed or can be compared with computer simulations of the 360 degree pendulum. Because of the large change of potential energy, the velocity of the bob changes significantly when it is given just enough energy to undergo full circular oscillations.

  • G1-17: PENDULUM WITH LARGE-ANGLE OSCILLATION - PORTABLE

    G1-17
    Illustrate large-angle pendular oscillations and the 360 degree pendulum.
    The motion of a small-angle oscillation can be compared with large-angle oscillations. The motion of a 360 degree pendulum with just enough energy to execute complete circles can be observed or compared with calculations.

  • G1-18: PENDULUM WITH FORCE SCALE

    G1-18
    Show the tension in the string exerted by a swinging pendulum.
    The spring scale reads the tension in the string as the pendulum swings, about 25 Newtons at the center and 19 Newtons at the ends of the swing with a bob mass of 1.1 kG. In this setup: F (center) = mg + mrw^2 = mg (3 - 2 cos a) F(end) = mg cos a where by conservation of energy m v^2 /2 = m r^2 w^2 /2 = mgr (1 - cos a) m r w^2 = 2mg ( 1 - cos a)

  • G1-31: HOOKE'S LAW AND SHM

    G1-31
    Quantitatively demonstrate how the spring constant affects the period of a mass on a spring.
    Determine the spring constant from the relationship F=kx using various numbers of 200 gram weights hanging from the spring. Hang groups of 200 gram weights from the spring and create vertical oscillations, obtaining the period using the manual timer. Compare with the period calculated from the relation T = 2 pi SQRT (m/k), where k was obtained above. This can be compared with actual integration of the equations of motion using a computer if desired.
    FS1, ME1

  • G1-32: MASS ON SPRING - WITH STAND

    G1-32
    Illustrate SHM.
    Mass moves up and down on spring with top end fixed to stand.
    FS1

  • G1-33 MASSES AND SPRINGS WITH SPIDER

    G1-33
    Compares frequencies of various mass-spring combinations
    Hang various masses on various springs and observe the oscillations. Notice that the damping is greater for the mass on the rubber band.
    FS1

  • G1-34: AIR TRACK - SIMPLE HARMONIC MOTION

    G1-34
    Demonstrate simple harmonic motion of a mass held by two springs.
    The center (moveable) glider, connected by springs to two fixed gliders (taped to air track), executes SHM about its equilibrium position when displaced and released. Additional weights can be taped to the oscillating glider to increase its period.

  • G1-35: MASS ON SPRING - EFFICIENT MODEL

    G1-35
    Illustrate the motion of a mass on a spring.
    Just lift mass and release to start oscillations. This one is relatively efficient, so its vibrations last a long time.
    FS2

  • G1-36: MASS ON SPRING WITH FORCE MEASUREMENT

    G1-36
    Display the time dependence of the force of a mass oscillating on a spring.
    A mass hangs on a spring that is in turn hanging from a spring scale. When the mass is raised and released, executing SHM, the force as a function of time (or position of the mass) is displayed by the spring scale.
    FS1

  • 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