A spring-mass system consists of a spring of stiffness 20 N/mm and a mass 12.74 kg, which can slide on a dry horizontal plane surface with coefficient of friction 0.32. The mass was displaced a distance 39 mm to the right of the frictionless equilibrium position and then released with zero initial velocity. Determine: a) The frequency of vibration. b) The position of the mass after a half cycle. c) The position of the mass after one cycle. d) The reduction of the strain energy in the spring during the first cycle. e) The work done by the friction force during the first cycle. f) The position and time at which the mass stops.

A spring-mass system consists of a spring of stiffness 20 N/mm and a mass 12.74 kg, which can slide on a dry horizontal plane surface with coefficient of friction 0.32. The mass was displaced a distance 39 mm to the right of the frictionless equilibrium position and then released with zero initial velocity. Determine: a) The frequency of vibration. b) The position of the mass after a half cycle. c) The position of the mass after one cycle. d) The reduction of the strain energy in the spring during the first cycle. e) The work done by the friction force during the first cycle. f) The position and time at which the mass stops.