Consider a mechanical system whose equations of motion are given by M1?x+B1?x?+K1?x?B2?z?=fo?(t)M2?x?+K2?x+M2?z?+B2?z?+K2?z=0? where K1?,K2?,M1?,M2?,B1? and B2? are known positive constants and x and z are displacement variables. Take the output of the translational mechanical system with output y=M1?x?+M2?(x?+z?), and input u(t)=f0?(t). Find a solutionspile.com

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Consider a mechanical system whose equations of motion are given by

M_{1} \overset{x}{¨} + B_{1} \overset{x}{?} + K_{1} x ? B_{2} \overset{z}{?} = f_{o} (t) M_{2} \overset{x}{?} + K_{2} x + M_{2} \overset{z}{?} + B_{2} \overset{z}{?} + K_{2} z = 0

where

K_{1}, K_{2}, M_{1}, M_{2}, B_{1}

and

B_{2}

are known positive constants and

x

and

z

are displacement variables. Take the output of the translational mechanical system with output

y = M_{1} \overset{x}{?} + M_{2} (\overset{x}{?} + \overset{z}{?}),

and input

u (t) = f_{0} (t)

. Find a state space model for this mechanical system based on the given equations of motion (pick an appropriate set of states). The equations of the state space model must be written in matrix notation.

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