What is the best way to plot the movement of a vibrating gas turbine blade?

Hello,

I need to create a plot to show the movement of a point on a vibrating gas turbine blade, and I would like to pick the most sensible (i.e. fastest, most versatile etc.) way.

The model is very simple, and in 2 dimensions (y,z). There are three separate components of motion:

1. the turbine is obviously rotating, so there is an angular velocity omega*r;
2. a vibration imposed on the y-coordinate, such as y=A*sin(omega*t);
3. a vibration imposed on the z-coordinate, such as z=A*sin(omega*t).

I want an output as a function of A and omega, and I thought about a function like

function [y,z]=motion(A,omega)

The output set of coordinates should then be interpolated to get a curve. I would also like to plot the inner and outer edges (two circumferences) of the blades on the plane.

Is this the best way? If possible, I would also like to get an output compatible with and straightforwardly usable in TikZ.

Any suggestions are highly appreciated.

Thanks very much