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Problem 1: Consider the mechanical system show below that consists of an upward bar with mass M and length 2a that rotates about its bottom point O with rotational viscous friction coefficient b,, A mass m is attached at the top of the bar and a horizontal force f(t) is applied on the mass. A spring k and a damper b are attached at the middle point of the bar as shown. The bar is initially at the vertical equilibrium position. Derive the linearized equation of motion of the bar with respect to its angular displacement 0(t). m M k