Most likely a simple spark plug misfire. Try changing plugs and possibly wires/rotor/distributor cap, whatever is recommended in your vehicles service manual.
You have a tire or tires out of balance.best to get tires road force balanced.
possibly a broken or missing engine mount
have your front tires rebalanced.
major vacuum leak?
A car can shake because of a problem in the transmission although this usually is not the problem. I will assume it shakes while it is idling or just starting out. It can also shake due to broken motor or transmission mount(s), bad u joints, a loose harmonic balancer, an unbalanced driveshaft or problems in the rear differential.
The car might need a tuneup . also the problem might be related to fuel injectors that are not working properly.
cause they do
A shake that is that speed sensitive is usually a bent rim, or bad tire.
Bad tires and bad alignment can cause the car to shake at certain speeds.
Shake the vechicle
yes
Filling your fuel tank will not make your car shake, unless you got some bad fuel that was contaminated with moisture.