We explore the physics of an atomic force microscopy (AFM) cantilever tip interacting with a generalized viscoelastic sample containing an arbitrary number of characteristic times, when the cantilever's base is driven with constant velocity toward the sample. This mode of operation, often called static force spectroscopy (SFS), can be harnessed to thoroughly analyze time-dependent viscoelastic information frequently overlooked in experiments. We generalize the solution of previous authors who have studied the standard linear solid model, and offer a solution applicable to any linear viscoelastic model. This generalization is crucial for the prediction of the model's response over wide ranges of time-scale. As a demonstration, successful predictions of harmonic functions (e.g., loss tangent) over a wide frequency range are obtained through analysis of simulated SFS results. In addition, we show that analysis through the generalized solution and previous expressions is no longer valid when the force does not grow linearly in time, so we also deliver an alternate route for extracting the viscoelastic information, which does not rely on the force linearity assumption. Despite the large amount of theoretical content (included for theoretical rigor's sake), the practical user can also benefit from the new procedures offered and the corresponding explanations. (c) 2017 Wiley Periodicals, Inc.