Simulation of Pendulum Waves: How it worksDescription| How it works
To model the motion of the pendulums, the small angle approximation formulae is used (commonly taught in high school physics). Details of these are available at this wikipedia page. A good discussion on the mathematics behind the pendulum waves can also be found on this blog. One end of the pendulum is fixed at the origin. The formulae in columns E and G calculate the X and Y positions of the other end of the penulum. We need the X and Y positions because Excel does not have a built in polar chart.
A simple macro increments a counter hidden behind the RUN button to simulate time. Note that this "time" is not the clock time, it is adjusted to get a good visualisation of the motion. The same file may run at different speeds depending on the CPU speeds too. The speed can be changed by changing the delay in the Run macro. Note the use of the DoEvents in the macro - this command enables the Excel sheet and chart to be updated.