Originally Posted by lucid
Let's think this through together Swamp...
In a static scenario, if one wants to evaluate the "stiffness" of the whole assembly, one would compress it a known distance, hold it there, and measure the force required to hold it there. Since static means that the distance between the mounting points of the assembly is constant, relative velocity of those points would be 0, and the damping ratio would not affect the force measurement, and one can obtain an overall k for the assembly, which should be pretty close to the k of the coil spring unless there are other parts in the assembly that act like springs.
In a dynamic scenario, I think I see what you mean since for the damper F=bv, and velocity is obviously not zero. So, the question is how stiff does that "feel" to the driver? It seems to me that, technically speaking, it is just as stiff, meaning k is k, but the force experienced by the driver is less since Power into the damper is F^2/b.
What do you think?
I think you are making it too complex. Statically you are correct, but what is ever static in a car - almost nothing! I love the math and equations (probably more than most) but this is simple. When you increase the damping of a shock but make no change to the spring the car feels stiffer. There is more reaction force from the shock (damper) and less suspension travel for a given fixed input (force (=bump)). Hence there is more acceleration (i.e. the suspension "shock" that you can feel in your rear) and is both qualitatively and quantitatively "stiffer".
By the way the k of the suspension aseembly is not close to the k of the spring. The multi-link lever system creates a significant mechanical advantage.