Question: 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}),

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 $F_{\text {control }}(t)$.

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