ANN: Simple Pendulum Simulation

[Roger Guay]

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


On Oct 31, 2005, at 2:32 AM, use-revolution-request at lists.runrev.com  
wrote:

> If you have the inclination, you might want to tackle the large
> amplitude pendulum. There is no nice analytic solution but you could
> numerically integrate the equation of motion. Something like this:
>
> Let A represent the angle. Then you  would do a numerical  
> integration with
>
> repeat loop
>    set the location of the pendulum to R,A --using radial coordinates
>    add c *  sine(A) to the angular velocity -- where c depends on the
> mass, L and  g
>    --The angular acceleration is proportional to  the torque which is
> proportional to sine(A)
>    --For small amplitudes sine(A) = A, in radial coordinates
>    add the angular velocity to A
> end repeat loop
>
> Where I have assumed the time interval between loops is one second,
> so that dt =1
>
> It would be interesting to show how the period (determined by the
> number of loops between changes in sign of the angular velocity)
> depends on the amplitude. Show that the clock slows down as it runs
> down, i.e. the period decreases with decreasing amplitude--albeit
> slowly; it is a second order effect in the amplitude. That's why
> pendulum clocks work so well.
>
> Jim