Example $23\mathrm{.}14.$ A coil of spring stiffness $4$ N$/$mm supports vertically a mass of $20$ kg at the free end. The motion is resisted by the oil dashpot. It is found that the amplitude at the beginning of the fourth cycle is $0\mathrm{.}8$ times the amplitude of the previous vibration. Determine the damping force per unit velocity. Also find the ratio of the frequency of damped and undamped vibrations.