# Doubochinski's Pendulum

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The Doubochinski's Pendulum demonstrates the discovery by Danil and Yovak Doubochinski that amplitudes in particular macroscopic oscillating systems will quantize. A magnet is secured to the end of a low friction pendulum arm and the arm is placed directly over an electromagnet. Regardless of where the pendulum initially starts its oscillation, it will settle at the closest amplitude out of 30, 43, 53, and 59 degrees due to the fact that the electromagnet only acts as an external force on the pendulum oscillation when the swing is within the electromagnetic field (zones 2 and 3).

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## Step 1: Power Rail/Virtual Ground

The power rail provides a virtual ground which will act as the ground for the rest of the circuit stages and isolates the DC to AC function generator from the power source.

## Step 2: DC to AC Function Generator

The function generator takes the DC voltage from the power rail and creates a sine wave to power the electromagnet using a cascade of op amps. The first stage created a square wave, which feeds into the inverting input of the second stage to create a triangle wave. The triangle wave feeds into the inverting input of the third stage to create a sine wave, which finally feeds into the inverting input of the fourth stage which acts as a feedback amplifier to amplify the sine wave. The final sine wave feeds into the base of a 2N3904 NPN transistor emitter follower circuit which acts as a current amplifier so that the current is high enough to create a proper electromagnet.

## Step 3: Solenoid

To create a solenoid, Secure one end of magnet wire to a 20mm or so diameter object (a glue stick or thick marker works quite well) and wrap the wire around the object, counting 70-100 turns (more turns for thinner wire, less for thicker) so that the solenoid is 50mm long. Make sure the solenoid is wrapped tight, so that there are no spaces between turns and no turns overlap. Secure the other end. If you wish to remove the object from the inside of the solenoid (although it should have negligible effect on the magnetic field as long as the object is nonmagnetic), you can do so by wrapping tape all around the outside of the solenoid so that it does not loosen or unwind, and then carefully sliding the object out. Place tape on the inside just as you did around the outside to ensure windings are secure. Finally, using a piece of fine sandpaper, remove the colored insulating coating from both ends of the solenoid to allow for proper conduction.

## Step 4: Assembly

Connect one side of the solenoid to the emitter of the current amplifier and the other side to ground. Secure a light magnet to the the end of a pendulum arm (around 100mm long) and place so that the lowest part of the pendulum is directly over the solenoid. The pendulum, if initially at rest, should gradually begin to oscillate and increase amplitude until 30 degrees amplitude is reached. If the initial position is an amplitude greater than 30 degrees, the amplitude will oscillate undampened once it dampens to 30, 43, 53, or 59 degree amplitude depending on the starting position.

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## Discussions

Fun experiment! This would be neat to use in a science class. :)