Answer Happy

June 2022 QUESTION 1 Consider an inclined bar made of two sections of length L₁ connected to a spring of constant ka and length L₂ connected to a damper of constant c₁ such that the co-linear sections is initially at a rotation of Bo 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 Do 0 H L3 A 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 ka. Considering the above system, determine the following information: 1.1 1.2 The equation of motion of the rotating rod in the form megata + Cegd + kein (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 + 25w₂0 + ²0 = 0 by manipulating the equation of motion if L₁ = 0.400 m, = 0.550 m, L3 0.420 m, ki 0.720 m, L4 = 0.630 m, L5 - 800 N/m, L₂ k3 = 2450 N/m, C₁ = 450 Ns/m, b = 0.065 m, w = 0.037 m, and = 22⁰ respectively. Total Marks: [18]