Hand damping of a vibrating string or membrane

Question

Problem is the following: If I have a guitar string or a drum membrane which is vibrating (and thus creating sound), when I place my hand or finger on it looses energy quickly, and  eventually silences.

Now, when I want to model this, I can add a drag force $f_{drag}$ to the wave equation

$$\frac{\partial^2 u}{\partial t^2}-c^2\nabla^2u=f_{drag}$$ which would be non-zero only on the place where my hand is put.

Question is: for this kind of damping, what would be the correct $f_{drag}$ (linear to the speed, quadratic to the speed, or something completely different)?