In this paper we revisited phenomenological potentials. We studied S-wave heavy quarkonium spectra by two potential models. The first one is power potential and the second one is logarithmic potential. We calculated spin averaged masses, hyperfine splittings, Regge trajectories of pseudoscalar and vector mesons, decay constants, leptonic decay widths, two-photon and two-gluon decay widths, and some allowed M1 transitions. We studied ground and 4 radially excited S-wave charmonium and bottomonium states via solving nonrelativistic Schrodinger equation. Although the potentials which were studied in this paper are not directly QCD motivated potential, obtained results agree well with experimental data and other theoretical studies.