The tree can be frozen by pushing a knot on its base. During the Marauders time at Hogwarts, a transformed Peter Pettigrew, whose Animagus form was a rat, would slip in and push the knot.

How do I turn off Whomping Willow?

However, there is a way to temporarily paralyze the tree. There is a particular knot on the trunk which can be pressed using a long branch in order to stop the attacks (PA18).

How did Harry and Hermione get past the Whomping Willow?

A moment later, the large black dog that's been stalking Harry shows up, nabs Ron, and drags him into the Whomping Willow. ... Harry and Hermione are able to use the secret passage under the tree (the one that showed up on the Marauder's Map, that no one could get to).