For the inverted-pendulum system shown below, assume that the mass of the inverted pendulum is M/4 and
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For the inverted-pendulum system shown below, assume that the mass of the inverted pendulum is M/4 and evenly distributed along the length of the rod. Also assume that the center of gravity of the pendulum is located at the center of the rod. If θ is small,
a) Derive mathematical models of the systems in the forms of differential equations
b) Derive related transfer functions
c) Determine state-space equations
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