I have a 2002 Cadillac Deville recently I had valve cover gaskets done. Since then every time I drive my car I can feel a vibration threw the gas pedal as if the motor mounts are broken. When I drove the car there it was fine but driving home after I could feel it. Question : do you have to disconnect anything like that either motor mounts or trany mount , when changing valve covers on the 2002 Cadilliac Deville ?

SOURCE: how to replace valve cover gasket on a 2002 stratus 3.0 liter engine

i don't know that vehicle very well... but there are usually bolts/screws that hold them in place. 4 to 6 of them per cover. sometimes the spark plug holes have giant nuts that hold the cover in place.

SOURCE: ENGINE VIBRATION AT IDLE BUT OK WHILE DRIVING.

Could be any one, or more, of the following -

Plugged injector
Bad plug wire
Fouled plug
Crossed plug wires (hard to tell sometimes on V-8s that run smooth anyway)
Vacuum leak
Leaky EGR valve
Shifted timing sensor

Scan engine for codes and proceed from there.

There is a product called RXP (available here in Texas) that will clean up an engine and gas. Its pretty awesome stuff, and this coming from a person who doesn't really believe in additives.

SOURCE: 2000 toyota corolla ce motor trembling when on drive holding down brakes.

check the brake disks. surface should be cleaned. also check the brake pads.

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92 accord loss power and shake

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Yes it can be related. If you bought the car from a car lot you may have a window sticker showing a 30 to 90 day warranty. The Catalytic converter can be expensive although it is similar to installing a muffler or header extensions.

The hesitation can be due to the engine controls trying to adjust for the difference in exhaust readings from one side to the other. Or it has excessive backpressure caused by the plugged catalytic converter.