A method of stability analysis called the τ-decomposition method is briefly described first. It is then applied to a two-degrees-of-freedom model. The effect of different amounts of damping and the effect of different amounts of deviation from tangency for the follower forces are taken into consideration. The results are given in a series of graphs showing the regions of asymptotic stability in the force amplitude-time delay parameter plane. One important result is that when the time delay is small and the force is compressive, the presence of a very small time delay could be enough to cause instability if the damping is small. The results obtained here for the case of zero damping agree with those given in [10], which is restricted to the undamped case, and also utilized a different method. The application given in this paper clearly demonstrates the effectiveness and simplicity of the τ-decomposition method and its superiority over other methods for dealing with retarded dynamical systems of this kind.

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