A simple system is represented by the governing equation

\[ m \ddot{x}+k x=F(t) \]

where \(m=1 \mathrm{~kg}, k=10 \mathrm{~N} / \mathrm{m}\), and \(F(t)=\cos t\) \(\mathrm{N}\), with zero initial conditions. Find the steadystate response \(x_{s}(t)\). Now suppose that the system is constrained regarding its maximum allowable amplitude, \(\left|x_{\max }\right| \leq 0.05 \mathrm{~m}\). Determine the needed \(F_{\text {control }}(t)\).