agitar

zarandear

agitar is the general word for shaking, like agitating a liquid or shaking a flag; zarandear specifically means to shake someone roughly, grabbing and jostling them.

trepidar

trepidar means to shake or tremble intensely, like an earthquake or vibrating machinery; agitar is more general.

sacudir

sacudir is a very common word for shaking, like shaking out a rug; agitar is more about stirring or agitating, often liquids or emotions.

menear

menear means to shake or wiggle something, often in smaller movements, like a dog wagging its tail; agitar is broader.