The theoretical basis is established for a general way of determining mechanical material properties from the measured response to impact at two different cross-sections of a linearly viscoelastic rod specimen. The measured quantities can be either strains or particle velocities. Explicit results are provided for two special cases, the first corresponding to a pre-existing method and the second to a new method. The results obtained under various conditions with the same material are in good agreement. The two methods usefully complement each other as well as other methods in a frequency range of approximately 20 Hz-20 kHz.