It could be your motor mounts, or it could be that you have used bad fuel, you could also have bad air filter or spark plug/s or one of your sensors is not functioning...give it a full tune up and if it still has the same faults, diagnose it with the scanner
you might have a router or caliber gone
It must be the rear brakes at fault.
if you car shakes when its fully stopped it may be the harmonic balancer, take it to a garage. is it shakes only when you are braking while stopping than have you brakes checked
If the steering wheel shakes, but to car doesn't, when applying brakes - your front rotors are warped (if you have disc brakes)...if you have drum brakes, the drum could be cracked or the pads worn unevenly If the whole car shakes, and the steering wheel only seems to react to that, when applying brakes - see above statement, but apply to the rear end. If the whole car shakes, including the steering wheel - all four corners are bad, and you're an accident looking for a place to happen soon. In any case, go to your nearest service center ASAP.
You went thru a deep puddle with hot brakes. The disc gets doused in cold water and warps.
the brake rotors are warped. resurface or replace rotors. if the vehicle shakes without applying the brakes, check tire balance.
Vibration when applying brakes is most likely warped rotors. Another cause could be loose caliper bolts.
2 possible issues, warped brake disc, or failing steering dampner.
Shakes, quivers, fluctuates, reverberates, trembles, resonates, oscillates...
Warped rotors
Good question. You may have an antilock brake circuit that is not sensing the brakes correctly and improperly correcting. Anti lock pulses the brakes when you apply them. I don't know if this is perfected or not.
Generally if it only shudders when braking then you likely have warped brake rotors but it could potentially be one of many other issues too.