Given is the following 2-dof system with m_1=80 \text{kg}, m_2=8 \text{kg} , k_1=200 \frac{\text{N}}{\text{m}}, k_1=125\frac{\text{N}}{\text{m}}, c_1=0, c_2=0.6\frac{\text{Ns}}{\text{m}}.
The system matrices are given by
| \begin{bmatrix} m_1 & 0 \\ 0 & m_2 \end{bmatrix} \ddot{\mathbf{u}}(t) + \begin{bmatrix} c_1 & -c_1 \\ -c_1 & c_1 + c_2 \end{bmatrix} \dot{\mathbf{u}} (t) + \begin{bmatrix} k_1 & -k_1 \\ -k_1 & k_1 + k_2 \end{bmatrix} \mathbf{u}(t) = \mathbf{0} . |
Determine all eigenfrequencies and mode shapes of the system.
Plot the system response in time domain given the initial conditions u_1(t=0)=1, u_2(t=0)=-1.