Comparing a real experiment to a simulation helps to see how our mathematical models relate to the practical situation, so I've been trying to build simulations for all of the practicals in my programme. Today I tried to simulate the flying pig practical. This one is quite difficult since it's 3 dimensional but I thought I'd have a go using geogebra. First I got a particle to move in a circle by defining the coordinated of a point in terms of the displacement of a particle travelling in circular motion.
x = rcosωt y = rsinωt
Then I wrote an expression for r in terms of ω by considering the forces acting on the pig.
This seemed to work in that as I made ω bigger the radius increased but there are problems:
when ω is small you get to a point where L2 is smaller than g2/ω4 and r becomes undefined.
the radius becomes almost equal to the length of the string even for not very large values of ω.
It seems that although the equation is satisfied for all motions of the pig it can't be used to predict all possible motions.
Here is my attempt
Having thought about this problem it is clear that the equation doesn't apply for small frequencies, the minimum frequency must be set so that L2 = g2/ω4 . I chose a value of = 3m and set the minimum frequency to 0.287656 Hz to prevent the square root going negative. The result looks promising:
