The position of the bead is given by two coordinates : phi and rho - angle and radius in polar coordinates.
The 2x 2nd order Equations of motion are derived with Lagrange2 formalism.
In order to be solved numerically by matlab buildin ODE solvers the equations have to be
linearized to 4x 1st order ODE's as follows:
w - angular frequency
y0=[0.01 0 0 w]; % [ r dr/dt phi dphi/dt ] initial conditions at t=0
tspan = [0 60];
f=@(t,y)[y(2);w^2 * y(1) ; y(4);0];
[t,y]=ode45(f,tspan,y0); % call ode45 solver
The .zip file contains a mp4-video of the animation.