Coupled Oscillations and Resonance

Rotating Saddle

Mechanical analog of a Paul Trap particle confinement—a ball is trapped in a time-varying quadrupole gravitational potential.

How it works:

A large saddle shape (attached to a plywood disk) is mounted on a multi-purpose turntable. The saddle shape is essentially a quadrupole gravitational potential. Rotation of this potential subjects the ball to an...

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Inverted Pendulum

A physical pendulum finds stability in its inverted position when driven at the proper frequency and amplitude combination.

How it works

The physical pendulum is a 45 cm x 2 cm x 6 mm (1/4") strip mounted on a ball-bearing pivot and can rotate 360 degrees. Its pivot is driven by a 3/4" stroke Sears Craftsman Auto Scroller Saw (model 315.172090) at about 50 Hz. The basic idea...

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Frahm Resonance Gyroscope

Vibrational resonances of metal reeds are excited by a spinning gyro as it slows down.

How it works

The Frahm resonance gyroscope is a standard piece of equipment that can be purchased from science supply houses. 1 It consists of a heavy wheel slightly unbalanced, held in a frame to which seven metal reeds are attached, each having a different vibrational frequency. The wheel is set in motion by unwinding a string that has been wrapped around the axle. As the wheel runs down, it sets each reed successively into vibration as its rotational frequency passes through...

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Big Chladni Plate

What it shows:

A large square metal plate, supported and harmonically driven at its center, is made to vibrate in any one of its numerous normal modes of vibration. As with the regular Chladni Plates, the two-dimensional standing wave patterns are made visible by sand accumulating along the nodal lines. What is different in this demonstration is that a multitude of resonances (across the entire audio range and lower ultrasonic frequencies) can easily be excited. Being a two-dimensional oscillator, the various resonance frequencies are not simply multiples of the...

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Chladni Plates

Accumulation of sand at nodes of vibrating plate reveals resonance patterns.

What It Shows

A Chladni plate consists of a flat sheet of metal, usually circular or square, mounted on a central stalk to a sturdy base. When the plate is oscillating in a particular mode of vibration, the nodes and antinodes that are set up form complex but symmetrical patterns over its surface. The positions of these nodes and antinodes can be seen by sprinkling sand upon the plates; the sand will vibrate away from the antinodes and gather at the nodes.

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Barton's Pendulum

Ten coupled pendulums of different lengths; shows resonance and phase.

What it shows:

All objects have a natural frequency of vibration or resonant frequency. If you force a system—in this case a set of pendulums—to oscillate, you get a maximum transfer of energy, i.e. maximum amplitude imparted, when the driving frequency equals the resonant frequency of the driven system. The phase relationship between the driver and driven oscillator is also related by their relative frequencies of oscillation.

How it works:

Barton's Pendulum...

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Shattering Wineglass

Large speaker with signal generator/amplifier destroys a wineglass; stroboscopic illumination shows vibration mode.

What it shows:

Sound waves of the right frequency are used to excite a wineglass in one or two of its normal modes of vibration. Stroboscopic illumination makes it possible to actually see the vibrations in apparent slow motion. When the intensity of the sound is increased, the large undulations of the glass exceed its elastic limit and cause it to shatter. This can be done in the fundamental or next higher normal mode of vibration ... a beautiful and dramatic...

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Chaotic Pendulum

Coupled, double, physical pendulum executes chaotic motion when non-linear initial conditions are imposed.

What it shows:

A double pendulum executes simple harmonic motion (two normal modes) when displacements from equilibrium are small. However, when large displacements are imposed, the non-linear system becomes dramatically chaotic in its motion and demonstrates that deterministic systems are not necessarily predictable.

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