(Solved):   7. The mass matrix, stiffness, and damping matrices of a two DOF system are, respectively, ...

 

7. The mass matrix, stiffness, and damping matrices of a two DOF system are, respectively, \[ \mathbf{M}=\left[\begin{array}{ll} 1 & 0 \\ 0 & 2 \end{array}\right], \quad \mathbf{K}=\left[\begin{array}{cc} 10 & -5 \\ -5 & 20 \end{array}\right], \mathbf{C}=\left[\begin{array}{cc} 0.1 & 0 \\ 0 & 0.3 \end{array}\right] \] The external harmonic force is \[ \mathbf{F}(t)=\mathbf{F}_{0} \sin \left(\omega_{e} t+\varphi_{0}\right) \] where \( \omega_{e}=3, \varphi_{0}=-0.7 \), and \[ \mathbf{F}_{0}=[-1,0]^{T} \] Determine the steady-state response of the system (10 pts).