Carbon bicycle frames have the unusual property that they are superior to aluminum frames in high-frequency absorption. A cyclist on a carbon-frame bike will feel tarmac chatter far less than on an aluminum-frame bike. The frame yields at these high frequencies, isolating the rider from them.
Yet carbon frames are also famously solid. A carbon-frame bike remains solid underneath a cyclist using arm muscles, efficiently transferring all their power to the drivetrain with little perceptible frame bending.
How can a material be good at damping, yet also be strong?
Credit for this phrasing of the question goes to TimWescott.