I've read a couple of threads like this recently but bottom line is yes, you're under damped.
Koni yellow can be a good choice because you can adjust rebound.
Check out the threads about various dampers and their damping curves in this forum that's helpful to understand.
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2017 M550i | Sophistograu
Previous cars: 2014 F30 ActiveHybrid 3 | 2012 f20 M135i
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