Pendulum project update

[Andreas Raab]

Hi Bert,

> I guess you are a little bit blinded by all the math. It's really 
> simple - the acceleration of the pendulum depends on its position. If 
> it is vertical, you have zero acceleration (because the force of 
> gravity is straight down and does not cause the pendulum to 
> swing). If it is horizontal, you have the maximum acceleration,
> again because the force points straight down, but now this is
> exactly the direction to make the pendulum rotate.

Exactly right.

> This trivially maps to an etoy (just increase the speed by the 
> acceleration value), the only obstacle is to get the acceleration 
> depending on the current angle. This is what the "weighing angles" 
> discussion was all about. Either you do this (best for 5th graders I 
> guess), or you "measure" it, like in the pendulum project I sent last 
> week. It works fine without any trigonometry or square roots: You 
> basically just take the _horizontal_ extent of a line that represents 
> your pendulum. If the line is vertical, its horizontal extent 
> is zero. If the line is horizontal, its horizontal extent is maximal. 
> You still need a sign for the force, which you can get by checking
> the extent relative to the line's reference point.

That's a little too abstract for my taste. One really needs to explain why
the relation between gravity and pendulum is not strictly linear because
otherwise you can do a very reasonable first order approximation of a
pendulum by simply subtracting its direction from gravity's direction. Note
that this fulfills all your constraints: It's zero if the pendulum points
into the same direction as gravity and it increases up to 90 degrees.

I've attached a project with this (wrong!) model to illustrate the fact. And
my challenge is: Explain why this can't be correct (heh, heh ;-)

Cheers,
  - Andreas
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