Shake is a general word that means that an object is making small sudden movements. Tremble is used when somebody shakes with small movements, because he/she is angry, excited or afraid. Shiver is used when somebody shakes with small movements, because he/she is cold or frightened.
shake Her body was shaking when she entered the court. What’s the matter? You are shaking! During the earthquake the whole building shook. tremble Her lips started to tremble and then she started to cry. What’s the matter? You are trembling! Mary was so angry that she trembled with rage. shiver We stood shivering in the cold air. When she saw the dentist, she started to shiver.