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QUESTION 1 Consider an inclined bar made of two sections of length L₁ connected to a spring of constant ki and length L₂ connected to a damper of constant e, such that the co-linear sections is initially at a rotation of 0 to the horizontal that is connected to a pivot and then allowed to rotate by a small clockwise angle as shown below. C1 L2 k₁ L₁ S ww 00 0 m L3 k3 L5 LA Attached perpendicular to the intersection of sections L₁ and L₂ is another section of length L3 to which is attached at its end point a rectangular planar mass of mass m with a breadth of b and a width of w. When the mechanism rotates by a clockwise angle a wire rope connected to the center-of-mass of the planar rectangle pulls a spring of spring constant ką. Considering the above system, determine the following information: d²0 do 1.1 The equation of motion of the rotating rod in the form meg da + Ceq dt + kegin (15) terms of the available information using kinematics and Newtons equations; The natural angular frequency wn and damping factor of the rotating rod if (3) 0 + 2Cwn0+w²0= 0 by manipulating the equation of motion if L₁ = 0.400 m, 1.2 = = = = L2 0.550 m, La = 0.420 m, k₁ 800 N/m, 0.037 m, and 0o = 22° 0.720 m, L4 0.630 m, L5 k3 2450 N/m, C₁ = 450 Ns/m, b = 0.065 m, w respectively. b W B Total Marks: [18]