Why is my cat shaking all over?
There are several reasons why a cat might tremble.
The first reason is that the cat's body is cold and the outside temperature is low. In this case, the cat may shiver. There is no need to go to the hospital. Just prepare a comfortable and warm environment for the cat. 
The second possibility is that the cat is in a new environment or has encountered unfamiliar people, which makes it nervous and causes it to tremble with fear. In this case, you can consider changing the cat's environment or providing some soothing guidance. The cat will calm down once it has calmed down.
The third possibility is that the cat may have an illness and is in pain, which is causing the trembling. In this case, you should not take it lightly and should take the cat to the vet immediately.