As I was watching this I kept on checking myself to see if I had any questions, but I wasn’t finding myself particularly pained by any of them (how periodic is his swinging? how long is the period?)
If instead of height from the ground we were plotting distance from the middle, maybe we could have somebody running from far away at a constant speed towards the middle of your swing. I think then there would be a pretty irresistible question that could be solved as a system of a linear-trigonometric equations.
Wicked cool, especially the last six seconds. A lot of kids just “stop” the graph at a point when that sort of thing happens. I have used this example with my kids but only as thought experiment. What do people think about offering the thought experiment version to kids first, then the video version a few minutes later?
I always had the impression that this kind of pendulum swing wasn’t a true sinusoid in the height function — that you spent more time at a low height than at the peaks. Looking more carefully, it appears the graph drawn in this video isn’t a true sinusoid but for a different reason: when you’re pushing forward there is less time taken on the downswing because velocity is higher.
So I’d be really curious for a super slo-mo “zoomed in” version for the first 4 or 5 seconds of this thing…
Are you using After Effects for the animations? Cause it looks great. I keep telling myself I need to get it but the price and the learning curve have kept me at bay. Any thoughts on the learning curve?
@Matt & Alex, yeah, that’s AfterEffects right there. The price is worse than the learning curve, which is also kind of annoying. I can’t imagine working without it, though. Alex, I reckon I’ll tutorialize this at some point soon.
@Jim, you’ve nailed what’s so freaking rich about these videos. You tweak the y-axis even slightly and you get a mind-bending new problem from a context the students already know.
@Bowen, going in, I was aware this wasn’t a sinusoid, true or otherwise. I may not have represented that well, though.