If the mass is changed hanging on a conical pendulum, will theta change?

I understand that the time period is independent of the mass, but theta is also dependent on the radius and height of the conical pendulum, which will surely change when the mass changes?

Also, if you are given the angular speed of the pendulum (omega or w) how can you test if the string of the pendulum is strong enough to support the mass?

Surely you don't need to use omega and just see if the string can freely support a weight of (mg/cos[theta]) where m is the original weight and g is gravity

Please refer to this diagram #

http://upload.wikimedia.org/wikipedi...ndulum.svg.png