A rotating machine component has an eccentricity of approximately \(e=0.1 \mathrm{~mm}\) in its center of mass resulting in a harmonic load on the structure. Assume, using the notation of the chapter, that \(m_{0} / m=0.05\), operating frequency \(\omega_{r}=100 \mathrm{rad} / \mathrm{s}\), \(\zeta=0.10\), and \(\omega_{n}=10 \mathrm{rad} / \mathrm{s}\).

(a) Solve for the amplitude and phase of the response in the form of Equation 3.53.

(b) Suppose amplitude \(A\) must be reduced by \(15 \%\). What options exist if actively controlling the structure is not one? Discuss which parameters need to be changed.

= x,(t) Asin(wrt 0), (3.53)