A wooden rectangular prism of mass \(10 \mathrm{~kg}\), height \(1 \mathrm{~m}\), and cross section \(30 \mathrm{~cm} \times 60 \mathrm{~cm}\) floats and remains vertical in a tub of oil. The frictional resistance of the oil can be assumed to be equivalent to a viscous damping coefficient \(\zeta\). When the prism is depressed by a distance of \(15 \mathrm{~cm}\) from its equilibrium and released, it is found to reach a depth of \(14 \mathrm{~cm}\) at the end of its first cycle of oscillation. Determine the value of the damping coefficient of the oil.