Question No$\mathrm{.}15$: A vibrating system consists of a mass of $8$kg$,$ spring of stiffness $5\mathrm{.}6$N$/$m and dashpot of damping coefficient of $40$N$/$m$/$s$.$ Find,$($i$)$Critical damping coefficient$($ii$)$ the damping factor$($iii$)$the natural frequency of damped vibration$($iv$)$the logarithmic decrement$($v$)$the ratio of two consecutive amplitude$($vi$)$the number of cycles after which the original amplitude is reduced to $20$ percent.