  (abridged) We develop a model which describes the coevolution of the mass
function of dense cores and of the IMF in a protocluster clump. In the model,
cores injected in the clump evolve under the effect of gas accretion. Accretion
onto the cores follows a time-dependent accretion rate that describes accretion
in a turbulent medium. Once the accretion timescales of cores exceed their
contraction timescales, they are turned into stars. We include the effect of
feedback by the newly formed massive stars through their stellar winds. A
fraction of the wind's energy is assumed to counter gravity and disperse the
gas from the protocluster and as a consequence, quench further star formation.
The latter effect sets the final IMF of the cluster. We apply our model to a
clump that is expected to resemble the progenitor clump of the Orion Nebula
Cluster (ONC). Our model is able to reproduce both the shape and normalization
of the ONC's IMF and the mass function of dense cores in Orion. The complex
features of the ONC's IMF,i.e., a shallow slope in the mass range ~0.3-2.5
Msol,a steeper slope in the mass range ~2.5-12 Msol, and a nearly flat tail at
the high mass end are reproduced. The model predicts a 'rapid' star formation
process with an age spread for the stars of 2.3 10^5 yr which is consistent
with the fact that 80% of the ONC's stars have ages of <=0.3 Myr. The model
predicts a primordial mass segregation with the most massive stars being born
in the region between 2-4 times the core radius of the cluster. In parallel,
the model also reproduces, simultaneously, the mass function of dense cores in
Orion. We study the effects of varying the model parameters on the resulting
IMF and show that the IMF of stellar clusters is expected to show significant
variations, provided variations in the clumps and cores properties exist.
