Convert the state space model of the MEMS device of Problem 8.6 and shown in Figure 8.32 into the…

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Convert the state space model of the MEMS device of Problem 8.6 and shown in Figure 8.32 into the corresponding transfer function matrix model by means of analytical derivation. Use MATLAB® to confirm the analytical result. Known are  damping coefficients   tiff ness of beam springs k1 = 2 N/m and stiffness of middle spring k = 3 N/m.

Problem 8.6

The MEMS system of Figure 8.32 is formed of two shuttle masses m1 and m2 coupled by a serpentine spring and supported separately by two pairs of identical beam springs. The shuttle masses are subjected to viscous damping and acted upon by two electrostatic forces f1 and f2. Use a lumped-parameter model of this MEMS device and obtain a state space model for it by having an output vector formed of the two masses’ displacements and velocities.