For a single degree of freedom spring-mass-damper system with \(m=2 \mathrm{~kg}\), \(k=1 \times 10^{7} \mathrm{~N} / \mathrm{m}\), and \(c=200 \mathrm{~N}-\mathrm{s} / \mathrm{m}\), complete the following for the case of forced harmonic vibration.
(a) Calculate the natural frequency (in \(\mathrm{rad} / \mathrm{s}\) ) and damping ratio.
(b) Plot the Argand diagram (real part vs imaginary part of the system FRF).
(c) Identify the point on the Argand diagram that corresponds to resonance.
(d) Determine the magnitude of vibration (in \(\mathrm{m}\) ) for this system at a forcing frequency of 2,000 rad/s if the harmonic force magnitude is \(100 \mathrm{~N}\).