1. A liquid supply mechanism comprising:a lower cover having a liquid outlet;
an upper cover connected to the lower cover, a chamber being formed between the lower cover and the upper cover, the chamber communicating with the liquid outlet, the upper cover having an axial hole;
a plunger movably disposed in the chamber, the plunger having an axial rod, the axial rod being inserted into the axial hole;
at least one resilient member disposed in the chamber, opposite ends of the resilient member abutting against the upper cover and the plunger; and
a plurality of damping members disposed on the axial rod, wherein a number of the damping members abutting against an inner wall of the axial hole changes in response to a height of the plunger.