We present new results for an old model: an anharmonic solute linearly coupled to a harmonic bath. A comparison of numerical simulations of the classical mechanical absorption spectrum to the results of conventional perturbation theory and the instantaneous normal mode (INM) approximation shows that the INM performs poorly in the low-friction regime, but yields reasonable results in the high-friction regime, in which perturbation theory is inappropriate. An analytical theory for the line shape is formulated to describe the regime of intermediate friction, in which neither perturbation theory nor the INM approximation works well.