it is having a misfire im guessing, is it vibrating all the time?
No, they do vibrate to a degree as they are generally mounted to the engine and it vibrates but it should not vibrate due to its operation.
Yes, bad spark pugs or plug wires can cause the engine cylinder to misfire which will cause the engine to vibrate.
could be a broken engine mount.
Could be a misfire. In need of a tune up.
motor mounts
A 1994 Corolla engine may vibrate if the motor mounts need to be replaced. The motor mounts can be purchased at any auto parts store.
It is idling. This is hard for an engine to do smoothly.
Possible bad motor mount
thermal energy
It is the engine that is vibrating and it is just being felt in the steering wheel. Can be a vacuum leak, or miss in the engine.
The engine is running rough. Could be in need of a tune up.
The engine is running C O C K