The mode shapes of an un-damped two degrees of freedom system are $\{1 \quad 0.5\}^{T}$ and $\{1-0.675\}^{T}$. The corresponding natural frequencies are $0.45 \mathrm{~Hz}$ and $1.2471 \mathrm{~Hz}$. The maximum amplitude (in mm) of vibration of the first degree of freedom due to an initial displacement of $\{2 \quad 1\}^{T}$ (in mm) and zero initial velocities is_____________

The mode shapes of an un-damped two degrees of freedom system are $\{1 \quad 0.5\}^{T}$ and $\{1-0.675\}^{T}$. The corresponding natural frequencies are $0.45 \mathrm{~Hz}$ and $1.2471 \mathrm{~Hz}$. The maximum amplitude (in mm) of vibration of the first degree of freedom due to an initial displacement of $\{2 \quad 1\}^{T}$ (in mm) and zero initial velocities is_____________

127