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Consider an inclined bar made of two sections of length L₁ connected to a spring of constant k₁ and length L2 connected to a damper of constant c₁ such that the co-linear sections is initially at a rotation of o 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 00 L3 L5 X 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 k3. Considering the above system, determine the following information: d²0 de 1.1 (3) 1.2 The equation of motion of the rotating rod in the form meq di + Ceq dt + keq in (15) terms of the available information using kinematics and Newtons equations; The natural angular frequency wn and damping factor of the rotating rod if 0 + 25wn0 + w²/20 = 0 by manipulating the equation of motion if L₁ = 0.400 m, L2 = 0.550 m, L3 = 0.720 m, L₁ = 0.630 m, L5 = 0.420 m, k₁ = 800 N/m, k3= 2450 N/m, c₁ = 450 Ns/m, b = 0.065 m, w = 0.037 m, and 00 = 22° respectively. m b W k3 w

Supplied Applicable Formulae for Question 1 Iy = 1/2m (b² + w²) I|| = Icom +md² k с mä +ci+kx = 0 +2¢wnx + w²/x = 0, wn -,S m 2mWn << 1 ⇒ x = x = C[exp(-(wnt)] [sin (wat +)], wd = Wn √1-5² v = [Cwa cos(wat +) - (Cwn sin(wat + y)] e¯ e-swnt " =