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Ten pendulums swing back and forth at slightly different rates, determined by the length of the strings. Starting in sync, the pattern shifts over time, until finally the pendulums realign.
Note that this Snack is constructed in four parts. In Part I, you’ll cut the PVC and mark the locations of the holes from which the pendulums will hang. In Part II you’ll drill holes in the pipe. In Part III, you’ll add the pendulums. In Part IV, you’ll finalize assembly and set the Pendulum Snake in motion.
Part I: Cut the PVC and Mark the Locations of Holes
Set aside all but the longest length of pipe. The other pieces will be used to construct the frame in Part IV.
Part II: Drill the Holes
Note: A drilling jig will hold the pipe steady, keeping it from rolling while you work and protecting the surface beneath it. If you don’t have a drilling jig, you can make one by hot-gluing scrap blocks of wood to a base, and then clamping the jig to a table or drill press (see photo below).
You can either drill both sets of holes at once (see Option A below), or you can drill one side, turn the pipe, and drill the other (see Option B below). Use Option A if you have access to a drill press and are familiar with its use, or if you are confident in your ability to drill almost perfectly vertically with a hand-held drill. (An inexpensive drill guide may help.) Otherwise, use Option B.
At each mark on the middle line, drill 1/8-inch (3 mm) holes through the top wall of the pipe and continue drilling through the bottom wall.
At each mark on the middle line, drill 1/8-inch (3 mm) holes through the top wall of the pipe. When you’re done, rotate the pipe so the line of holes you drilled sits on the bottom of the pipe. Then, on the top of the pipe (directly above the set of holes you just drilled) draw a straight line the length of the pipe and mark it in exactly the same way you did in Step 3 above. When you’re done, drill 1/8-inch (3 mm) holes at those marks, as you did on the opposite side of the pipe.
Part III: Add the Pendulums
Note: If you don’t have a tapestry needle, straighten out a paper clip and use a small piece of masking tape to hold the wire and string together.
Part IV: Assemble the Frame and Set the Pendulum Snake in Motion
To do this, measure from the bottom of the PVC pipe, midway between the two hanging strings, to the center of the hole in the hex nut (the hex nut’s center of mass). When the pendulum is the correct length, firmly tighten the screws, leaving any extra string in place.
Face the row of pendulums and use the wooden board to pull them all towards you simultaneously (see photo below). Flip down the board to get it quickly out of the way, and then sit back and watch the show!
At first, all the pendulums move together. Then a snake-like pattern emerges (see left photo below), dissolving into a random mess. Next, the pendulums alternate and move in perfect opposition (see right photo below). The random mess reappears, eventually followed by a return to the original perfect alignment. Then the whole cycle repeats.
If you don’t see these patterns, try “tuning” the pendulums by adjusting their lengths slightly. If a particular pendulum is arriving too soon at the moment when everything should be synced, then lengthen it a little; if it’s arriving late, then shorten it a little. Adjust the string length by loosening either screw, shifting the string, and then retightening the screw.
Each pendulum swings back and forth at a slightly different rate, determined by the length of string supporting it. This causes them to fall out of step with each other as they swing.
At certain time intervals, however, the balls fall into recognizable patterns. For example, after 15 seconds, neighboring pendulums are one half-swing apart, causing them to swing in perfect opposition. After 30 seconds, the balls line up again and the cycle of patterns repeats (see table below).
People are often surprised to learn that the time it takes a pendulum to swing back and forth—called the pendulum’s period—doesn’t depend on the mass of the pendulum bob or on how far the pendulum swings.
You can prove this to yourself by swinging a bottle of water on a string: First try it with a full bottle, then dump out half of the water. Then try little swings and big, wide swings. Does the pendulum’s period change?
Math Root
The equation for the period (T) of a simple pendulum is:
where T is the period in seconds per swing, L is the length (in meters) and g is the acceleration due to gravity (9.8 m/s2).
The frequency F of a pendulum is the number of times it swings all the way back and forth in one second (expressed in swings per second). Frequency is the inverse of period, or 1/T. So the equation for calculating the frequency of a pendulum is the inverse of the formula above, or
Squaring both sides,
Solving for L,
You can use this equation to calculate the length of a pendulum for a given frequency. For example, the longest pendulum of your Pendulum Snake swings back and forth 24 times in 30 seconds. Frequency is expressed in swings per second, so 24 swings/30 seconds = 0.8 swings/second. Using 9.8 m/s2 for g and 0.8 swings/second for F in the equation gives you a length of 0.387 meters, or 38.7 centimeters.
Check out this episode of Build Your Own Exploratorium to see this Snack in action.
Two pendulums influence each other’s motion to create Intriguing patterns.
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Attribution: Exploratorium Teacher Institute