This week, I figured it out: the sensor is the ball. I attached a string to a rotary motion sensor (so that I could determine the angle and angular v as a function of time) and hung the force probe from it.
Puling it back and letting it swing, I got a good data set, even though I couldn't effectively zero the rotary motion sensor for some unknown reason.
To get the model to work without the rotary motion sensor being zeroed, I added an offset to the formula when I created a calculated column in Logger Pro. Once I did that, we could compare the graphs of actual tension (red) and predicted tension (pink):
There's an interesting time offset that I haven't explained yet: ideas?