We have obtained exact analytical expressions in closed form, for the linear
modes excited in finite and discrete systems that are driven by a spatially
homogeneous alternating field. Those modes are extended for frequencies within
the linear frequency band while they are either end-localized or end-avoided
for frequencies outside the linear frequency band. The analytical solutions are
resonant at particular frequencies, which compose the frequency dispersion
relation of the finite system.Comment: 4 pages, 3 figures, submitted to Phys. Rev.