high idle but runs good cold- when warms runs quite rough and smells like rubber burning under the hood- when warm the car's engine and exhaust shake and sometimes white smoke comes out the tailpipe-driving short distances stopping and starting adds to the problem

the engine seems to be shaken constantly, and the exhaust is shaking along with the engine. i don't know what could be the problem. i have tried new oil, but that has not done anything, and cannot remember doing anything stupid (i. e. going forty over a speed bump) that could have caused this annoying disturbance.