For a single degree of freedom spring-mass-damper system under free vibration, determine the values for the mass, \(m(\mathrm{~kg})\), viscous damping coefficient, \(c(\mathrm{~N}-\mathrm{s} / \mathrm{m})\), and spring constant, \(k(\mathrm{~N} / \mathrm{m})\), given the following information:
- the damping ratio is 0.1 - the undamped natural frequency is \(100 \mathrm{~Hz}\)
- the initial displacement is \(1 \mathrm{~mm}\)
- the initial velocity is \(5 \mathrm{~mm} / \mathrm{s}\)
- if the system was critically damped, the value of the damping coefficient would be \(586.1 \mathrm{~N}-\mathrm{s} / \mathrm{m}\).