Harmonograph

Overview

Build a fascinating device that uses pendulums to make art.

Background

For hundreds of years people have marveled at the weird patterns that can be drawn by a simple drawing device. Early inventors  made elaborate and creative devices. Later this tradition was reinvented with the “Spirograph” toy that accomplished the same patterns with a series of nested plastic gears. 

Science

Pendulums are swinging that hang from a pivot point. The length of the pendulum determines the period, that is it the time it takes to swing back and forth. The energy of the pendulum is provided by initially pulling the weight back and letting go. The pulling back adds gravitational potential energy to the system. As the pendulum swings it converts potential energy to kinetic energy of motion at the bottom of the swing. As the momentum carries the weight up again it converted once more to potential energy. Without adding new energy to the system the pendulum will gradually wear down due to friction. This means the arc becomes less and less with each stroke until it completely stops at the bottom. Throughout this process the period never changes. 

The length of the pendulum is partly determined by the center of gravity. So heavy weights placed at different places on the arm effectively change the length and period of the pendulum. A heavy weight increases the energy that can be stored in the system so the pendulum lasts longer on a starting swing.

When two pendulums interact they can pull on the resultant output to create an ellipse. If the periods are different, and the momentum of each pendulum is different then the ellipses change. Energy can also pass from one pendulum to the other. Periodic motion, changing speeds and gravity also guide the motion of the planets which is why planets have elliptical orbits which also slowly decay.

Materials / tools

• Sticks
• board
• nails
• Pens
• Water bottles 

Directions

1. Set up two pendulums at right angles to each other so they pivot on the edge of a board.
2. Attach weights to each pendulum at some point. You can use a water bottle or sand bag tied with a rubber band.
3. Tie a right angle arm to the extending part of each pendulum.
4. Attach a pen to the intersection of the two arms.
5. Balance the system so that the pen rests lightly on the paper
6. Pull back each pendulum and let go.

Fine Tuning

Friction at the pivot points slows the arms down. Friction can be reduced by having a sharp metal edge or point  that sits on a metal support point.

Resources