The point I have been trying to make is that the initial force transmitted to the vehicle body is greater when the damper is present than it would be if the damper was not present. Do you agree?
I question the supposition that the mass of the damper is significant for the purposes of this discussion - they seem pretty light compared to most of the other parts in consideration, and the force to accelerate the damper piston is certainly much smaller than the damping force "seen" by the suspension.
You are right that if you put a given amount of energy into the system, it must be split between the various storage / dissipation methods on the vehicle. I'm not so sure that the bump (forced displacement profile) represents a fixed amount of energy, but that's another discussion.
Let's take another simplified system, where we have a spring, a mass (vehicle), and a damper, where the spring and damper are connected in parallel and support the mass, and we apply a pulse to the bottom of the spring/damper.
* The energy stored in the spring increases as one end displaces relative to the other
* The energy dissipated by the damper is related to the velocity of one end of the damper relative to the other, the damping coefficient, and the distance that the damper displaces
* The energy stored in the vehicle is related to its velocity and its mass
A stiffer spring will displace less when the pulse is applied, resulting in greater energy transfer to the mass (and greater acceleration, velocity of the mass)
A larger damping coefficient will result in less displacement of the damper, resulting in greater energy transfer to the mass (and greater acceleration, velocity of the mass)
If you disagree, can you give me any real value of a damping coefficient for the damper that will result in more suspension deflection (less body deflection), on the first half of the pulse, than you would have with zero damping?