Using the Newmark method with \(\alpha=\frac{1}{6}\) and \(\beta=\frac{1}{2}\), solve Problem 11.20.

Data From Problem 11.20:-

The equations of motion of a two-degree-of-freedom system are given by \(2 \ddot{x}_{1}+6 x_{1}-2 x_{2}=5\) and \(\ddot{x}_{2}-2 x_{1}+4 x_{2}=20 \sin 5 t\). Assuming the initial conditions as \(x_{1}(0)=\dot{x}_{1}(0)=x_{2}(0)=\dot{x}_{2}(0)=0\), find the response of the system, using the central difference method with \(\Delta t=0.25\).