Question: For a certain dynamic system the state-variable equations for the position (x_{1}) and velocity (v_{1}) are given below: where (x_{2}(t)) is the input and the

For a certain dynamic system the state-variable equations for the position \(x_{1}\) and velocity \(v_{1}\) are given below:

x = V 1 mi -[-(k+k2)x1-bv + bx2+k2x2(1),

where \(x_{2}(t)\) is the input and the output is \(x_{1}\). Use the s-operator to obtain the input-output differential equation which relates the output \(x_{1}\) and the input \(x_{2}(t)\).

x = V 1 mi -[-(k+k2)x1-bv + bx2+k2x2(1),

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