Draw resonance onsets of actual viscoelastic spinning processes with secondary forces operated by constant draw ratio are determined via transient frequency response simulations under a constant tension or force boundary condition, which causes the system to be always stable. Transfer function data between the spinline velocity and the tension at the take-up position in the frequency domain, which are transformed from the transient responses of the take-up velocity with respect to a step change of the take-up force, play a key role in the determination of the onset points for various spinning cases. It is confirmed that the critical draw ratios established in this study are almost the same as those decided by linear stability or direct transient simulation methods for velocity-controlled spinning systems. The transfer function data for the stability analysis can be readily and beneficially applied to an analysis of sensitivity of a spinning process with respect to a sinusoidal disturbance. (C) 2015 Elsevier B.V. All rights reserved.