The landing gear of an airplane can be idealized as the spring-mass-damper system shown in Fig. 3.52 [3.16]. If the runway surface is described \(y(t)=y_{0} \cos \omega t\), determine the values of \(k\) and \(c\) that limit the amplitude of vibration of the airplane \((x)\) to \(0.1 \mathrm{~m}\). Assume \(m=2000 \mathrm{~kg}, y_{0}=0.2 \mathrm{~m}\), and \(\omega=157.08 \mathrm{rad} / \mathrm{s}\).

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y(t) x(t) (a) FIGURE 3.52 Modeling of landing gear. 00000 Wheel Runway Housing with strut and viscous damping Mass of aircraft, m