It will be some sort of hyperbolic function, and the force and length of rope will determine the frequency to predict the shape.  The initial 'circle' at your wrist will define the constant force to explain the sin curve.  This is not a very good explanation but if you were to define a hyperbolic function using a z axis it could be sinh z=(e^z-e^-z)/2.  

Shape of rotating rope (lasso problem?)
I have a 97 Honda Civic that will occasionally die in neutral. This is what I have done so far:


Replace both O2 sensors
Replace MAP sensor
Replace Air filter
Added Lucas treatment to fuel tank 


Even after the above changes, occasionally when coasting in neutral the rpm's will eventually drop to 0 and the engine will die. It starts back up just fine. My engine and fuel mileage have definitively improved with all the changes, especially after using Lucas.
