(Solved): Please show the answer in detail!! Q3) Calculate the constants \( \alpha \) and \( \beta \) for the ...

Please show the answer in detail!!

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 \( \zeta_{1}=\zeta_{2}=0.25 \).