For a spring-mass-damper system, \(m=50 \mathrm{~kg}\) and \(k=5000 \mathrm{~N} / \mathrm{m}\). Find the following:

(a) critical damping constant \(c_{c}\),

(b) damped natural frequency when \(c=c_{c} / 2\), and

(c) logarithmic decrement.