could be a few reasons, check out your suspension rods, the tie rod ends, or maybe see if your tires are balanced
im an auto technitian and it might be your alinment is off on either sides or both
If you are in Full time it is recommended not to go over 25mph that is probly why it shakes put it in part time you can go up to 55 mph in part time
If your car shakes while underway, your tires have worn incorrectly from misalignment. If it shakes while in park or not moving, your engine is misfiring.
If a car shakes during acceleration the brake rotors may be damaged. If the rotors are damaged they will be unstable as the tires rotates making the whole car shake.
If a car shakes and loses power when idling it can be the spark plug. If a spark plug is fouling, it can cause power losses.
Engine miss.
Warped rotors
Most likely the front wheel balance is at 40-50 and the rear wheel is at 60-65 Check these first at a good tyre dealer. Also check wheel alignment.
Car shakes when I put the brake check
When the engine light comes on and the car shakes at the same time, it could be the spark plugs or ignition coils are faulty. Misfiring is causing the car to shake.
Most likely your alignment is out of whack or bad struts. Could also be the wheels need balancing.
Disk brake rotor is warped