A dynamic absorber is to be designed to eliminate the vibration at coordinate \(x_{1}\) for the system shown in Fig. P5.6, where the excitation frequency is \(400 \mathrm{rad} / \mathrm{s}\) and the force magnitude is \(100 \mathrm{~N}\). For the given system constants, determine the values of the mass and spring constant for the dynamic absorber if the magnitude of vibration for the absorber mass is \(5 \mathrm{~mm}\).

Fig. P5.6 Single degree of freedom system excited by the harmonic forcing function \(100 e^{i 400 t}\)

Ix m 1004001