The harmonograph was invented in the nineteenth century. It draws pleasing patterns on paper using a pen linked to several pendulums.
This harmonograph has three pendulums. The pendulums are pivoted about a quarter of the way down. The top section of each pendulum above the pivot moves as the pendulum swings. One pendulum has a table attached to the top carrying a sheet of paper. The other two pendulums are at right angles to each other. The top of each pendulum is connected by a pivoted arm to a single pen that draws on the paper when the harmonograph is working. The pendulums can be changed in length. Changing the length will alter the time for one ‘swing’. This time is called the ‘period’ of the pendulum.
When the pendulums are moving and the pen is in contact with the paper, the harmonograph will draw a pattern.
The relative periods of the pendulums changes the patterns. When there are whole number ratios between pendulums, one gets the most pleasing patterns. For example, ratios like 2:3 or 1:2 work well. If we have one pendulum period of 1 second and another of 2 seconds, the results should be good.
Pendulum period is set by the length of the pendulum. The period is proportional to the square root of the length. If a 1 metre pendulum has a period of two seconds, then a pendulum which is 250cm (1/4 metre) long will have a 1 second period. In other words, to halve the period, the pendulum must be a quarter the length.
The reason for using heavy weights is to increase the time the pendulums swing. This will produce a figure with finer divisions between the lines. Small weights work, but friction lead to loss of energy and the size of the shapes quickly gets smaller compared to the behaviour with heavy weights. Friction occurs in the bearings needed at several points and where the pen touches the paper.
The way the pattern reduces in size and changes as it does so, makes it interesting to watch. This reduction in size happens as the energy in the pendulums is used up. The patterns may alter in various ways as the pattern gets smaller. This adds to the fascination.
Delaying the start of one of the pendulums by a small interval will affect the pattern. This is ‘phase difference’. It is another way to vary the result produced.
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