(Solved): Q3) Calculate the constants \( \alpha \) and \( \beta \) for the two-degree-of-freedom system given ...

Q3) Calculate the constants \( \alpha \) and \( \beta \) for the two-degree-of-freedom system given by \[ \left[\begin{array}{ll} 1 & 0 \\ 0 & 4 \end{array}\right] \ddot{\boldsymbol{x}}+(\alpha M+\beta K) \dot{\boldsymbol{x}}+\left[\begin{array}{cc} 6 & -2 \\ -2 & 2 \end{array}\right] \boldsymbol{x}=\mathbf{0} \] such that the system has modal damping of \( \zeta_{1}=\zeta_{2}=0.25 \).