>

>Thanks, Jim. I do indeed have this inclination. In fact my original

>intent was to use the simple pendulum to learn and apply the Runge-

>Kutta Method. I just haven't gotten around to it yet. Might your

>suggestion be a variation of this?

>

>Cheers, Roger

>

Roger,

Actually I was thinking of something even simpler than the

Runge-Kutta approximation.

Using the Euler approximation, the repeat loop to generate the

pendulum motion is really simple and looks like this:

repeat until the mouseClick

setRA r,270+psi -- Polar coordinates; 270 so that the pendulum hands DOWN

add -c*psi to angVel --Add angular acceleration to the angular velocity

add angVel to psi --Add angular velocity to the angle

end repeat

where psi is the angular displacement of the pendulum.

I am using Turtle Graphics, but I think you get the idea. To see this

in action, put this in the message box:

go stack url "

http://home.infostations.net/jhurley/ControlGraphics.rev"

and go to the last card.

Control graphics is a variation on TG. It allows you to identify any

control as a Turtle which not only responds to Transcript, but also

to TG. So you can create a circle graphic and call it "pendulum" and

then talk to the circle like it was a turtle, i.e. forward 10, right

90, setXY 20,30, setRA 200,35 etc.

Polar coordinates are particularly useful in the pendulum problem

I tried to show the dependence of the period on the amplitude but no

luck so far. Maybe Runga-Kutta is required.

The period depends on the amplitude (to second order in the

amplitude) in this way:

T = T(0) (1 + A^2/16)

where A is the angular amplitude in radians.

Jim

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