With this applet, you can investigate mass ratios that lead to stable ring systems vs. unstable ones. If the mass of each ring body is no more than 2.3 times the mass of Saturn divided by the cube of the number of ring particles, then the system can be expected to be stable; otherwise not.
For the derivation of this inequality, see:
Linear Stability of Ring Systems.Astronomical Journal, 133:656-664, 2007.

In the applet at left, M is the mass of Saturn (in Earth-masses), m is the mass of an individual ring body, and n is the number of bodies (including the central body).

The textfield labeled gamma is the ratio m*n^3/M. If this value is smaller than 2.3, the system will be stable. Large values will be unstable.

You will find that you don't need to increase m very much to make the system unstable. If you set "warp" to 100, the integrator will show the instability very quickly. Give it a whirl.

Note: the warp parameter only controls how often the screen is updated---large values mean that many time steps of the integrator are performed between each screen update. This makes the simulation run much faster as updating the screen image is more time consuming that a step of the integrator.