Calculate the damping ratio of the system shown if the weight and radius of gyration of

Question:

Calculate the damping ratio ζ of the system shown if the weight and radius of gyration of the stepped cylinder are W = 20 lb and k̅ = 5.5 in., the spring constant is k = 15 lb/in., and the damping coefficient of the hydraulic cylinder is c = 2 lb-sec/ft. The cylinder rolls without slipping on the radius r = 6 in. and the spring can support tension as well as compression.