We present theoretical and experimental results on the mechanical damping of an atomic force microscope cantilever strongly coupled to a self-assembled InAs quantum dot. When the cantilever oscillation amplitude is large, its motion dominates the charge dynamics of the dot which in turn leads to nonlinear, amplitude-dependent damping of the cantilever. We observe highly asymmetric lineshapes of Coulomb blockade peaks in the damping that reflect the degeneracy of energy levels on the dot, in excellent agreement with our strong coupling theory. Furthermore, we predict that excited state spectroscopy is possible by studying the damping versus oscillation amplitude, in analogy to varying the amplitude of an ac gate voltage.Coupling a nanomechanical object to quantum electronics provides a system that can be used to probe both the mechanics and the electronics with extreme sensitivity. It has been predicted that the electronics may be used to measure the quantum nature of the mechanical object [1], and the reverse-using the mechanics to measure the quantum nature of mesoscopic electronics-was recently demonstrated with superconducting qubits [2]. Electromechanical systems that have attracted considerable attention recently include quantum shuttles [3], and mechanics coupled to single electron transistors [4,5] or tunnel junctions [6,7]. In most systems studied both experimentally and theoretically, the interaction between the electronic and mechanical components is weak.In this paper we study strong coupling effects, both theoretically and experimentally, in an electromechanical system consisting of a quantum dot capacitively coupled to an atomic force microscope (AFM) cantilever. Electrons tunneling on and off the dot effectively damp the cantilever, and this damping exhibits Coulomb blockade peaks as a function of bias voltage similar to those well known in the dot conductance, even in the limit of weak coupling [8,9,10]. It has long been predicted that level degeneracy on the dot leads to lineshape asymmetry of Coulomb blockade peaks in the conductance [11]. Recently, we observed corresponding temperaturedependent peak shifts in the damping at weak coupling [10], but the lineshape asymmetry was far too small to be measured before now. However, by driving the cantilever to large oscillation amplitudes we enter a regime of strong coupling where its motion strongly modifies the tunneling rates on and off the dot, and leads to a dramatic enhancement of the lineshape asymmetry. This enhancement is much greater than expected from simply extrapolating the weak coupling theory; it is a non-adiabatic effect that stems from the similarity of timescales for dynamics of the cantilever and the dot. Furthermore, we predict that by measuring the damping versus bias voltage and oscillation amplitude, strong coupling provides a means to perform excited state spectroscopy on the dot. Note that very different strong coupling effects unrelated to degeneracy were recently reported for a driven carbon nanotube coupled to an embedded do...