This large pendulum demonstrates simple harmonic oscillations. Two bobs of different mass can be set with varying length. The audience will compare modes of oscillations and see how the frequency of oscillations depends on length and mass of the pendulum.

Pictures to the left show a standard rigid pendulum. The gravitational force F = mg is directed downward on the pendulum bob, and the restoring force on the bob is mg sinθ. When the plane of oscillation is rotated about the horizontal axis by angle φ (see pictures to the right), the gravitational force mg is replaced with mg cosφ. Therefore the restoring force is reduced to mg cosφ sinθ and the period of oscillation is increased to . In other words, the motion of the pendulum in its plane of oscillation is the same as if gravity were reduced by the factor cosφ.

To change the plane of oscillation the instructor should push a small rod on the mounting bracket with his/her thumb (as shown in pictures above). Students will see an immediate change in pendulum's period. To fix the angle of the plane, tighten the thumbscrews that anchor the pendulum mounting bracket to the degree plate.

Note: Position of the bob on the rod can be adjusted.

Two identical pendula are attached by a soft spring and exchange energy with each other. This demonstration is useful for elementary physics, mechanics, and particle physics. Instructor can show the audience normal modes with or without the spring.

Note: To release the spring, use the screwdriver attached to the frame.

The pendulum consists of a metal cylinder attached to a helical spring. This system can perform longitudinal and rotational oscillations which are coupled. The moment of inertia of the system can be adjusted with respect to the vertical axis.

Notes:

• When set in motion, the weight should go back and forth between completely rotational motion and completely vertical motion. If it never stops rotating, or going up and down, it must be adjusted by moving the discs. Start with each disc about 7 1/2 turns out from the cylinder, then make fine adjustments.
• This demonstration requires at least a 7 foot rod for suspension of the pendulum.

Different weights are hung from various springs of different strengths to demonstrate simple harmonic oscillations.

This demonstration shows the behavior of a bowed violin string. It is particularly popular among students who attend the course "Physics in Music."
The setup consists of the bowed string apparatus and an oscilloscope. The picture to the lower left shows the graphs of displacement and velocity of a bowed string. Its vibrations are very different from simple harmonic motion. Due to high static and low kinetic friction between the bow and string, the force applied by a player leads to a "stick and slip" motion which in turn distinguishes the bowed string's rich tone and ability to sustain notes.

How it works: When part of the string moves in a magnetic field (see picture to the right), it generates a weak current. The current runs through a simple electronic circuit, and provides a signal displayed on an oscilloscope. The circuit has two modes: displacement and velocity. The string should be musically tuned before the demonstration. Note: Apply liberal amounts of rosin to the bow

Beautiful patterns of sand (Chlandi figures) are formed on black thin metal plates as a result of standing waves.

A mechanical vibrator (see picture to the bottom left) powered by the functional generator provides oscillations to the rectangular or circular plates, attached at the center. Standing wave patterns only occur for certain frequencies and will form when waves in the plates are reflected at the boundaries. The center point is always a node for each standing wave. The vibrations of metal plates are heard but their amplitude is too small to be seen directly. To make the patterns visible, sprinkle sand on the plate. The sand will then be jiggled away from the parts of the plates in rapid motion and tend to fall along the nodal lines. Chlandi figures are admired by artists and used in violin and guitar construction.

We also have a large aluminum plate which can produce various Chlandi's figures when excited by a cello bow.

Notes: Do the demonstration in a clear plexiglass box to collect sand. Use a video camera for large classes.

This demonstration creates and projects large Lissajous figures on the overhead screen. The apparatus consists of a laser and mirrors mounted on two speakers. The frequencies and amplitudes of the mirrors' oscillations are adjusted on two separate functional generators that power the speakers. Students could see the Lissajous figures and hear the sound related to the sum of frequencies with the ratio 1:1, 1:2, 1:3, etc.

List of parts: Clear plexiglass box with two speakers and attached mirrors He-Ne Laser (5 mW) 2 functional generators

The demonstration helps to visualize the propagation of longitudinal waves. It is 1.1 meters long and consists of 21 veritcal rods connected to each other by soft springs and pivoting on a base. The picture to the right shows how it works.

To demonstrate the propagation of longitudinal waves, keep the slinky stretched between two wide-open hands on the table. Give the slinky a push along its axis; the spring will compress and dilate as the longitudinal wave travels through it. The speed of the wave is related to the spring's compressional resistance.

This rope is commonly used to demonstrate the properties of transverse waves. The rubber rope can be fastened to a vertical rod and stretched by hand. A single pulse or a short train of pulses can be sent down the rope by rapid hand motion.

By increasing the tension, the instructor can show the increase in wave velocity. Vertical or horizontal hand motion can launch vertically or horizontally polarized waves.

Properties of polarizers can be demontrated by shooting wave pulses of random orientation through a vertical grating (as shown in the picture to the far right). Waves polarized at, say 45 degrees, will be partialy transmitted with (more or less) vertical polarization. Due to friction of the rope against the rods, the demonstration of the partial transmission is not perfect, but illustrative.

Motor driven rubber rope can create 5- 5.5 m long patterns of standing waves of different frequencies. This demonstration consists of a long rubber rope clamped between two vertical rods, and an AC electrical motor controlled by a Variac. An aluminum wheel is attached to the shaft and provides reciprocating motion to drive the rubber rope. The setup is shown in the picture.

Notes:

• The frequency of oscillations (number of nodes and antinodes) is changed by the Variac.
• The rope should be taut (no slack) to achieve good patterns of standing waves.

Consists of 3 sections, each section has a large A-frame base with a series of steel rods attached at their centers to a torsion wire. This machine produces slow moving, high amplitude transverse waves and can be used to demonstrate:

• Wave propagation
• Wave length versus velocity and frequency
• Standing waves
• Reflection at fixed and free boundaries
• Constructive and destructive interference

Each section has rods of different lengths. Section one is 92 cm long with 46 cm rods. Section 2 is 92cm long with 23cm rods, resulting in a wave velocity that is 3 times as fast. Section 3 is 46cm long, with rods that vary from 23 to 46 cm. This section acts as an impedance matching unit. This set also includes clamps for ridged determination, a dash pot for liquid damping, and couplers for connecting sections together.

This is a very simple way to demonstrate standing and traveling waves by rotating the small handles on the side of the plastic box placed on an OHP.

Two clear plastic plates with concentric circles printed on them show wonderful interference patterns when placed on top of each other on an OHP. Changing distance between their centers produces different spreads of interference.

The ripple tank is designed for an OHP and creates wave patterns on water. It is equipped with an electronic ripple generator. The frequency, amplitude, and phase of the two actuators can be adjusted.

This demonstration explains the phenomenon of the "whispering galleries," where one can speak softly at one place and is clearly heard in a remote location. There is one such gallery at the Exploratorium in San Francisco.

The demonstration is based on an elliptical well containing water with a bit of dye. The two foci of the ellipse are marked. A disturbance at one focus from a drop of water or mechanical vibrator causes an identical disturbance at the other focus. Because of the properties of an ellipse, waves emanating from one focus and reflecting from any point on the wall of the well arrive at the other focus in phase. This is an example of constructive interference.

This demonstration also can be used for explanation of "quantum mirage." This effect describes a spot where electron waves are focused so they reinforce each other producing a virtual image of the original atom.