The hard part about understanding this is modeling the position of each pendulum easily. If you want something that cycles from 0 to 1 and back try: Absolute value of (x mod 2 + 1) note:drop the abs to see direction. If they all cycle in 60 seconds it's easy to see that any cycle will start over. At 1/2 the full cycle time they will split into left and right sides etc. Now, work backward after the fastest ball does 4 cycles you can see something that looks nothing like a sine wave.
However, you now need to substitute that position as time into the pendulum equation. At which point you see the sine wave behavior of sticking near the edges as the ball picks up momentum followed by a fast transverse through the center. Still, it's not really a sine wave but it's fairly close. To get a true sine wave all the pendulums would need to be the same length and the balls dropped the same distance but at slightly different times. However, in the experiment they are close to the same length and distance fallen so it looks about right.
However, you now need to substitute that position as time into the pendulum equation. At which point you see the sine wave behavior of sticking near the edges as the ball picks up momentum followed by a fast transverse through the center. Still, it's not really a sine wave but it's fairly close. To get a true sine wave all the pendulums would need to be the same length and the balls dropped the same distance but at slightly different times. However, in the experiment they are close to the same length and distance fallen so it looks about right.