Question: Find a suitable set of state variables, derive the state-variable equations, and form the state equation. (left{begin{array}{l}ddot{z}_{1}+dot{z}_{1}+frac{1}{2} kleft(z_{1}-z_{2} ight)=e^{-t / 3} z_{2}-frac{1}{2} kleft(z_{1}-z_{2} ight)=0end{array},

Find a suitable set of state variables, derive the state-variable equations, and form the state equation.

$\left\{\begin{array}{l}\ddot{z}_{1}+\dot{z}_{1}+\frac{1}{2} k\left(z_{1}-z_{2}\right)=e^{-t / 3} \\ z_{2}-\frac{1}{2} k\left(z_{1}-z_{2}\right)=0\end{array}, k=\right.$ const

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