rumbling noise and vibration for first 20-30 minutes of driving. on 2001 Ford Focus

A month ago I started hearing a rumbling noise when I start my car, as well as feeling vibrations in the car including under my foot when I push on the accelerator. This now happens every time I start my car when it is cold and goes away after 20-30 minutes. Is this serious? Is this an expensive type of repair?

Asked by for the 2001 Ford Focus
It is so hard to express an opinion on what the source of the noise may be without being able to hear the noise first hand or being able to drive the car and or do some tests. The noise could be an exhaust heat shield that has deteriorated or cracked, it could be a muffler or catalytic converter that has deteriorated and needs to be replaced or it could be the water pump or fan belt tensioner. It could be so many things ,safer to bring it somewhere to get it looked at in case neglecting to look at this noise now results in more expensive repairs down the road.