I am looking at a simple cantilever beam deflection:

I understand the general expression for deflection/force would be:

$y_s = \frac{Fx_s^3}{3EI}$

$F_p = \frac{3y_sEI}{x_s^3}$

If you were going to add viscous damping to the bending of the beam, would it be as simple as:

$F = \frac{3y_sEI}{x_s^3} - cEIθ_t$

Where the equation for the angle of deflection is $θ = \frac{FL^2}{2EI}$?

I have seen some suggestions that simple damping of cantelever beams is done by applying viscosity to the rate of angle change with respect to time. Is that generally correct?

I have had some strange behaviors trying this so I'm not sure what the ideal simple solution is.

Thanks for any help or answers/ideas for either question. It is appreciated.