Determine Critical damping co-efficient

Question

In a vibrating system a coil spring of stiffness 50 N/mm supports a vibrating mass of 250 kg at the free end. In addition the motion of mass is controlled by a dashpot whose resistance is proportional to velocity. From  measurement it is found that the amplitude at the beginning of the fourth cycle is 0.8 times the amplitude of the third cycle. Determine :

1. damping co-efficient of the dashpot.
2. Critical damping co-efficient.
3. The damping factor.
4. The ratio of the frequencies of damped and undamped vibrations.                

Answer 1

Given a Vibratory system