Below are a few pictures of the pendulum wave and release mechanism.
Pendulum wave at rest:
Release mechanism beginning to collect pendulums:
Just before releasing the wave:
About 30-35 seconds after release:
About Pendulum Waves
Pendulum waves are simply a series of pendulums that are pulled back, then released at some angle(s). If the lengths and angles are just right, then each pendulum will cycle back and forth between its release position at a slightly different frequency than its neighbor. This results in some pretty neat alternating waveforms. Wave pendulums make great desktop toys for your rich dads, and have even been known to keep children quiet for up to 60 seconds. In addition, the can make nice props in classroom settings for illustrating physics principles such as potential and kinetic energy, air resistance, aliasing, and more.
About the Uniqueness of My Pendulum Wave
To my knowlege, the design for the pendulum wave in this instructable is unique for a number of reasons. First, the wave is intended to be viewed primarily from the top rather than a side (although it looks cool from the side, too). Consequently, it is important that the amplitude of each pendulum appears the same from above. While this requires a more complex release mechanism (instead of the typical flat board), it also leads to a very cool look. As far as I am concerned, a little extra coolness is worth a little extra effort, any day.
In order to release the pendulums at the varying release angles required for a top view, I designed a very original release mechanism. Each arm of the mechanism grabs its respective pendulum at a different time. This creates a wave effect as the mechanism curves up and around the pendulums. Once all pendulums have been selected and brought to their proper positions, the mechanism releases them all at the same time, creating the pendulum wave. The math for this is a little tedious, but the concept is pretty straightforward.
Here is a very crappy SolidWorks video demonstrating two arms of the release module in action:
Here is an animation of the final design in action. Air resistance was neglected in this animation, which is why no damping occurs. However, since air resistance will not affect the period of the pendulum wave, that is fine.
Step 1: Where the Waves Come From
As I touched on already, a wave pendulum is a series of pendulums with incremented frequencies. One way to think of the pendulum wave is as a series of points used to sample a wave of increasing frequency. This effect is shown in the video below, which I created using Matlab:
The Nyquist Sampling Theory (NST) states that to sample a wave of a given frequency, one needs to measure points at one-half cycle of that frequency. Or, for a given frequency f, one needs points spaced 1/(2*f) units of time apart (since T = 1/f). When the number of sampling points becomes less than the number required by the NST, aliasing occurs. This aliasing is the reason for the alternating waveforms present in a pendulum wave.