The condition for the system in equilibrium is: Mg = m w[sup]2[/sup]r =m v[sup]2[/sup]/r .
The mass m is the same in the above simulation.

First right click to pause the simulation.
LEFT Click at the black dot (mass M) and drag it up and down, you will change r and M at the same time. (Keep the total length of the string the same).
There is no way to keep the system in equilibrium if you change radius r ,and keep velocity v and mass M remaining constant.

If you LEFT Click at the red dot (mass m) and drag the mouse, you will change velocity v and mass M at the same time. (keep r the same).

For your cases:
- the centripetal force as a function of mass M(with velocity v and radius r remaining constant)
[b] Then m is proportional to M.[/b]
- the centripetal force as a function of velocity v(with mass M and radius r remaining constant)
[b]Then m is proportional to v[sup]2[/sup][/b]
- the centripetal force as a function of radius r (with velocity v and mass M remaining constant)
[b]Then m is proportional to 1/r[/b]

Do you really want to simulate the above situations?