(Solved): Represent the translational mechanical system shown in Figure Q. 2 in state space equation, where x ...

Represent the translational mechanical system shown in Figure Q. 2 in state space equation, where $x_2(t)$ is the output and $f(t)$ is the input. Given spring constant as $k_1=1\mathrm{N}/\mathrm{m}$, mass $m_1=8\mathrm{kg},m_2=3\mathrm{kg}$ and damper constant as $f_{v1}=4\mathrm{Ns}/\mathrm{m},f_{v2}=16\mathrm{Ns}/\mathrm{m},f_{v3}=f_{v4}=$ $5\mathrm{Ns}/\mathrm{m}$. Determine the state space representation of the system using $x_1(t),x_2(t)$ and their first derivatives as state variables. [10 marks]