You need to check your brakes and rotors. Typically when the rotors go out it will make any car/ truck do that.
the braking system
You have a warped rotor. Brake pads need replacing and the rotors turned or replaced.
Warped rotor and worn out brake pads.
Check for warped front rotors. under slight brake application it may not shake. But under hard braking such as getting off an offramp the truck will shake and the brake pedal may pulsate slightly. Chances are real good this is your problem.
Probably warped brake rotors. They can be removed and resurfaced or replaced with new ones.
Be sure to check suspension components. Namely the tie-rods...
If it only happens when you are braking I would suspect warped brake rotors. Other reasons the front end could shake would include unbalanced tires or the vehicle needing realignment. Whatever the case may be; driving a car in this condition is unsafe and you should repair it or have it repaired before you drive it again.
An anti-lock braking system, or ABS (from the German, Antiblockiersystem) is a safety system which prevents the wheels on a motor vehicle from locking while braking. A rotating road wheel allows the driver to maintain steering control under heavy braking by preventing a skid and allowing the wheel to continue interacting tractively with the road surface as directed by driver steering inputs.
4 time ASE certified tech here, warped front brake rotors will make your brake pedal pulsate and steering wheel shake when braking. most noticed when moderate braking at 40 - 50 mph.
It is good practice while driving to accelerate while in a turn. This is because most cars have their brakes in the front wheels, and braking while in a turn will cause the rear of a car to go into a spin.
A car shaking while applying brakes is most likely caused by worn a brake pad. Check the brake system at all four wheels to find the problem.
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