Simple Harmonic (and non-harmonic) Motion

Tuning Forks

Selection of mounted tuning forks and rubber hammer.

How it works:

Each tuning fork is mounted on a wooden sound box to amplify the sound (they're very difficult to hear without the box). A microphone/preamp/scope setup may be used to visually demonstrate the pure sinusoidal sound wave. Additionally, a frequency analyzer shows a single frequency component (however, if the gain is turned up high, you may also see the frequency components due to the resonances of the sound box or harmonics of the tuning fork if it was whacked too hard). One of the...

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Driven Damped Oscillator

Single air track glider, with and without variable frequency driver, variable damping, and oscilloscope position vs. time display.

What It Shows

With one end of the car attached via a spring to the end of the track and the other end of the car coupled (via a similar spring) to a driving motor, we can see how the car behaves when it is driven below, at, and above the resonance frequency. Markings on the motor help to show the phase relationships between the driver and car at different frequencies. A storage scope tracks the motion of the car (see Setting It Up...

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Pendulum Waves

What it shows:

Fifteen uncoupled simple pendulums of monotonically increasing lengths dance together to produce visual traveling waves, standing waves, beating, and random motion. One might call this kinetic art and the choreography of the dance of the pendulums is stunning! Aliasing and quantum revival can also be shown.

How it works:

The period of one complete cycle of the dance is 60 seconds. The length of the longest pendulum has been adjusted so that it executes 51 oscillations in this 60 second period. The length of each...

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Torsional Pendulum

Oscillation of mass on wire in torsional mode of oscillation.

torsion pendulum

What It Shows

The frequency of oscillation of a torsional pendulum is proportional to the square root of the torsional constant and inversely proportional to the square root of the rotational inertia.

How...

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Physical Pendulum

A rigid rod executes simple harmonic motion about an adjustable pivot point.

What It Shows

The period of a physical pendulum is measured and compared to theory. The pivot point, and thus the period, is adjustable along the length of the pendulum making it possible to demonstrate that there is a pivot point where the period is a minimum (stationary point).

How It Works

The physical pendulum is a 1/2" diameter × 100cm long brass rod. A collar with a "knife edge" can be fixed anywhere along the length of the pendulum and serves as the pivot point. The period...

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Circular Motion and Simple Harmonic Motion

Simultaneous shadow projection of circular motion and bouncing weight on spring.

What It Shows

One of the simplest of periodic motions is uniform circular motion. By shadow projecting both uniform circular motion and oscillatory simple harmonic motion onto a screen, one can show that these two seemingly different kinds of motion are actually identical.

How It Works

A 8 cm diameter plastic ball mounted near the edge of a 46 cm diameter disk undergoes uniform circular motion. The disk, oriented vertically, is driven by a 57 RPM motor.1 A large...

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Simple Harmonic Motion Demonstrator

Relation between circular motion and linear displacement on overhead projector.

What It Shows

Uniform circular motion can be shown to be the superposition of simple harmonic motions in two mutually perpendicular directions. This apparatus gives the audience a visual display of how one dimensional simple harmonic motion varies in unison with circular motion.

...

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Reversible (Kater's) Pendulum

A physical pendulum with two adjustable knife edges for an accurate determination of "g".

What It Shows

An important application of the pendulum is the determination of the value of the acceleration due to gravity. By adding a second knife-edge pivot and two adjustable masses to the physical pendulum described in the Physical Pendulum demo, the value of g can be determined to 0.2% precision.

How It Works

Using a simple pendulum, the value of g can be determined by...

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