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In this paper results are presented from a study that investigates the use of centrifugally driven pendulum vibration absorbers for the attenuation of engine torsional vibrations. Such absorbers consist essentially of movable counterweights whose center of mass is restricted to move along a specified path relative to the rotational frame of reference. These devices are commonly used in light aircraft engines and helicopter rotors. The most common designs use a circular path for the absorber, tuned to a particular order of rotor disturbance, although more recent developments offer a wider variety of paths. Our goal here is to evaluate the system performance for a range of path types with different types of tuning. This analytical study is carried out for a simple mechanical model that includes a rotor and an absorber riding along a quite general path. Approximate solutions are obtained using a perturbation scheme and compared with detailed computational results.