A new type of flywheel energy storage system that has a horizontal axle with High $T_c$, superconductor bearings using Y123 single-domained crystals was developed.The dynamic Properties, stiffness and damping of the high $T_c$, superconductor radial bearings were experimentally estimated using a imbalance excitation method. The imbalance excitation method applied to this rotor- bearing system identified the identified stiffness and damping of the high temperature superconductor beatings to be 2.8 $3.3 { imes} 10^5 N/m and 775 204$ Nsec/m respectively.