A vibration system consists of a mass 50 kg, a spring of stiffness 30 kN/m and a damper. The damping provided is only 20% of the critical value. Determine (a) the damping factor, (b) the
critical damping coefficient, (c) the natural frequency of the damped vibrations, (d) the
logarithmic decrement and (e) the ratio of two consecutive amplitudes.

Agas contained within a piston-cylinder assembly e end nation about same energy states, 1 and 2, where pi 10 bar, v undergoes two processes, a and b, between the sam 0.1 m3, ui-400 kj and p2 1 bar, v2 1.0 m2, u2 200 kj: process a: process from 1 to 2 during which the pressure- volume relation is pv constant process b: constant-volume process from state 1 to a pressure of 2 bar, followed by a linear pressure-volume process to +20 0 state 2 kinetic and potential energy effects can be ignored. for each of the processes a and b, (a) sketch the process on p-v coordinates, (b) evaluate the work, in kj, and (c) evaluate process the heat transfer, in kj