Match the quantity with the appropriate units (units may used more than once, some units may not be used).

(a) The natural frequency, \(\omega_n\)
(i) \(\mathrm{N} \cdot \mathrm{m}\)

(b) The damping ratio, \(\zeta\)
(ii) \(\mathrm{rad}\)

(c) Damped natural frequency, \(\omega_d\)
(iii) None

(d) Logarithmic decrement, \(\delta\)
(iv) \(\mathrm{rad} / \mathrm{s}\)

(e) Phase angle, \(\phi\)
(v) \(\mathrm{Hz}\)

(f) Change in amplitude per cycle, \(\Delta A\)
(vi) \(\mathrm{m}\)
(g) Energy loss under a hysteresis loop, \(\Delta E\)
(vii) \(\mathrm{N} \cdot \mathrm{s}\)
(h) Hysteretic damping coefficient, \(h\)
(viii) \(\mathrm{m} / \mathrm{s}\)
(i) Initial angular velocity of torsional system, \(\dot{\theta}(0)\)
(ix) \(\mathrm{N} / \mathrm{s}\)