For a single degree of freedom spring-mass-damper system with \(m=2.5 \mathrm{~kg}\), \(k=6 \times 10^{6} \mathrm{~N} / \mathrm{m}\), and \(c=180 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), complete the following for the case of forced harmonic vibration.
(a) Calculate the undamped natural frequency (in \(\mathrm{rad} / \mathrm{s}\) ) and damping ratio.
(b) Sketch the imaginary part of the system FRF versus frequency. Identify the frequency (in \(\mathrm{Hz}\) ) and amplitude (in \(\mathrm{m} / \mathrm{N}\) ) of the key features.
(c) Determine the value of the imaginary part of the vibration (in \(\mathrm{mm}\) ) for this system at a forcing frequency of \(1500 \mathrm{rad} / \mathrm{s}\) if the harmonic force magnitude is \(250 \mathrm{~N}\).