A pendulum moving in two directions creates beautiful designs.
In this activity, a marking pen remains stationary while a platform swings beneath the pen, acting as a pendulum. As the platform swings, the pen marks a sheet of paper that is fastened to the platform, generating beautiful, repetitive patterns, which grow smaller with each repetition. These colorful designs contain hidden lessons in physics.
12 to 14 feet (3.5 to 4 m) of 1/2-inch Schedule 40 PVC pipe, cut into the following lengths:
Eight 5-inch (13 cm) lengths, four for attaching the hanging platform to the upright frame and four for the short sides of the base
Two 7-inch (18 cm) lengths, for the left and right top portions of the upright frame
One 4-inch (10 cm) length, for the center top portion of the upright frame
Two 21-inch (53 cm) lengths, for the long sides of the base
Three 18-inch (46 cm) lengths, two for the legs of the upright frame and one for the swinging arm of the penholder
Three 2-inch (5 cm) lengths, two for the hand-hold on the swinging arm of the penholder and one to insert in the penholder T-joint, so the pen fits snugly inside
Eight 1/2-inch PVC 90-degree elbows (to connect parts of the frame and the swing-arm; see photo)
Three 1/2-inch PVC T-joints (one to hold the marking pen; two to connect the vertical frame to the horizontal base)
One 3/16-inch (4.75-millimeter) wooden dowel, cut to about 6 inches (15 cm) long (for drawing-arm pivot)
Two 1/2-inch PVC crosses (supports for the hanging platform)
Five large binder clips (four to anchor strings; one to hold paper to platform)
Two mini or micro binder clips (to anchor dowel in drawing arm)
Four screw eyes (to connect string to hanging platform)
Drill bit, 13/64 inch (5–5.5mm)
PVC cutter, hacksaw blade, or other way to cut PVC pipe
Paper (anything will work, including clean sides of used copy paper)
Marking pens (Sharpie fine-point markers or similar), assorted colors
Four pieces of string, each approximately 2 feet (60 cm) long; cut off extra after assembly if necessary
A 10 × 10 inch (25 × 25 cm) platform board of some sort—particle board, plywood, or similar (see Assembly)
Optional: Masking tape to wrap around pen if needed for fit.
Note: Rather than providing detailed instructions for assembling this device, we have chosen instead to supply some close-up photos and the following helpful hints. The rest is left to the dedicated experimenter.
The penholder must be counterbalanced so that the pen exerts minimum pressure on the moving board while maintaining constant contact with the writing surface. The size and orientation of the pieces at the back end of the pen assembly can be adjusted to achieve a suitable balance.
To make the pen assembly shown in the photos, the pivot hole was drilled about 10 inches (25 cm) from the pen end. If the hole is drilled at a different location, the size and location of the mass at the far end of the arm should be adjusted accordingly.
The platform must have sufficient mass so that its motion does not die down too quickly. The platform shown in the photos is a 10 inch × 10 inch (25 cm × 25 cm) piece of 1/2-inch particleboard, which has a significant mass. If a lighter platform is used, a mass can be affixed to the platform. If the location of the mass is adjustable, you may find that its placement will affect the pattern obtained.
The Drawing Board should produce a pattern that repeats the same basic shape over and over again, with each cycle getting smaller. If the pattern is not consistent from one cycle to the next, try adjusting the counterbalance weight on the penholder. Experiment to see what works best.
Using binder clips allows you to adjust the four pieces of string so that the drawing platform hangs level (see photo below).
The wooden dowel for the drawing arm pivot is held in place with two mini or micro binder clips (see photo below).
A standard Sharpie marking pen will fit into the 1/2-inch PVC T-joint, but you can modify the holder to suit any size felt-tip marker. You can also adjust the fit of the pen by wrapping it with masking tape.
To Do and Notice
Once your Drawing Board is adjusted, you can create wonderfully intricate designs. Push the board to start rotational as well as translational motion; lower the pen to start drawing and raise it to stop. Try drawing one to four patterns on the same paper using pens of different colors, changing the direction and force of the push with each new color.
What's Going On?
When you push on the platform, displacing it from its resting position, the four suspending strings exert forces on it to bring it back. You can think of these forces as acting in two directions perpendicular to each other: north-south and east-west, for example. The combination of these two simultaneous motions can produce a variety of curved forms, in the same way that careful use of the two knobs on an Etch-a-Sketch toy allows you to draw curves.
The diminishing size of each successive repetition of the pattern is a graphic demonstration of how friction steadily dissipates the energy of a moving object.
Some of the shapes you will produce with the Drawing Board are known as harmonograms, or Lissajous figures. An oscilloscope can easily produce these figures because the pattern on the scope face is generated by a single electron beam simultaneously moving vertically and horizontally on the screen. An oscilloscope can be thought of as an electronic Etch-a-Sketch.
One of our teachers had this Snack set up and running during an aftershock of California’s 1989 Loma Prieta earthquake. The pen traced the pattern of motion generated by the aftershock. The operating principle behind the Drawing Board—a pen directly attached to the earth with a paper only loosely attached to the earth—is the operating principle behind the seismograph.