If want to know how fast a wet dog should shake in order to dry, you must watch this video. If you don't want to, you must watch anyway: It's full of cute furry animals shaking in slow motion.
You can fast forward through the formulas for the money shots.
A team lead by Georgia Institute of Technology's Andrew Dickerson have discovered the universal formula that rules the shaking-to-dry frequency of furry animals. Well, kind of, because it still has correction issues that may be explained by the length of the animal's fur.
What they found
First, the team filmed and analysed the motion of dogs shaking the water off. They found, for example, that a labrador retriever shakes his body at a frequency of 4.3Hz while a small husky does it at 5.8Hz.
Looking at the frequency difference, they realised that the shaking speed was connected to the radius of the animal's body. Water is attached to the dog by surface tension, they thought, and the sinusoidal shaking creates centripetal forces that ejects that water off the body. Therefore, the larger the dog's body radius (R) is, the stronger these forces are on the dog's skin.
This means that smaller furry animals would have to shake faster to achieve necessary forces, which is why a mouse has to shake at 27Hz, while a cat does it at 6Hz. Looking at this data, they found out that the frequency had to be the R^0.75, with the "shake frequencies asymptotically approach 4Hz as animals grow in size".
The team found out that, while this law is true, there's a correction factor missing, which may be related to the fur itself. I'd imagine that the length, type and morphology of the hair would play a role in all this as well.