Here is the F vs D plot where step 1 up to 0.1 s is gravity ramping up while the top rail is held fixed, then step 2 is the bottom rail moving up 30 mm. You can see that about 3 N is perfect force to be in the middle of the flat region.
Checking the mass, it is at the sweet spot of 0.30 kg.
Adjusting the mass up just slightly causes a gravity powered Static Structural solution to shoot well past the middle and end up on the far end of the flat. It is very difficult to adjust the mass to put it on the flat, especially with the wavyness.
To answer your question on Damping, you should watch the videos in this course: