Act-and-wait concept in control theory is a tool for enhancing the control quality by decreasing the destabilising effect of time delay. As was shown in other works, applying the act-and-wait concept to a PD position control increases the available range of proportional gains, which reduces the steady-state error of dry friction. In this paper, we focus on the vibration phenomena at the boundaries of the dynamic stability from the aspect of the vibration spectrum. We consider a single-degree-of-freedom mechanical model of DC actuators that contains significant effective damping. At different types of stability limits, new analytical and semi-analytical results are derived for the vibration spectrum. The results are validated by numerical calculations and experiments on a linear DC actuator.