This animation was produced in response to a video of real pendulums performing similar tricks:

Not having an animation program I thought I’d use the finite element program Strand7. Modelling the pendulums was easy, just 15 beam elements with a “translational mass” attribute on the end (more on the exact length of each pendulum later).

Strand7 Pendulum Model

Strand7 will perform a dynamic analysis, so I could have given each pendulum a displacement and then carried out the analysis of their movements over 90 seconds, but because I was only interested in generating the patterns in this case I decided to take the easy way out and generate the pendulum movement by inputting the displacements directly. The procedure was:

Set up 30 “freedom cases”, each with the lower end of a different pendulum given a unit deflection in the X or Y direction

Set up a series of 1800 increments, corresponding to time steps of 1/20 second, and factor each freedom case to replicate the pendulum motions.

Run the analysis

Create an animation of the resulting pendulum motions, using an end on view as in the original video

The only remaining problem was how to enter 1800 x 30 factors quickly and accurately. The solution (naturally) was to set up a table of the X and Y displacements of each pendulum in Excel:

Freedom case factor table

These factors were then transferred into Strand7 using the program’s API (the use of which I will describe in more detail in later posts).

The only remaining detail was to find the correct pendulum lengths to generate the patterns I was after. After a little experimentation it became clear that each pendulum much have a different integer number of cycles over some fixed period. I fixed the first pendulum length at 350 mm, which has a period of 1.187 seconds, or 51 cycles over 60.558 seconds. The other pendulum lengths were then adjusted to have 52 to 65 cycles over the same time period, giving a range from 336.7 mm to 215.5 mm.

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