The acceleration theorem for wave packet propagation in periodic potentials disentangles the k-space dynamicsand real space dynamics. This is well known and understood for Bloch oscillations and super Blochoscillations in the presence of position-independent forces. Here, we analyze the dynamics of a model system inwhich the k-space dynamics and the real space dynamics are inextricably intertwined due to a position-dependentforce provided by a parabolic trap.We demonstrate that this coupling gives rise to significantly modified and richdynamics when the lattice is shaken by a modulated parabolic potential. The dynamics range from chirpedBloch-harmonic oscillations to asymmetric spreading oscillations. We analyze these findings by tracing thespatiotemporal dynamics in real space and by visualizing the relative phase in the k-space dynamics whichleads to an accurate explanation of the obtained phenomena. We also compare our numerical results to a localacceleration model and obtain very good agreement for the case of coherent oscillations, however, deviations foroscillations with spreading dynamics which altogether supports the interpretations of our findings.