Consider an inclined bar made of two sections of length L₁ connected to a spring of constant k₁ and length L₂ connected

[answerhappygod]

Consider An Inclined Bar Made Of Two Sections Of Length L Connected To A Spring Of Constant K And Length L Connected 1 (92.15 KiB) Viewed 53 times

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 c such that the co-linear sections is initially at a rotation of fo 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 k3 L5 L4 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: 1.1 The equation of motion of the rotating rod in the form med + Ce+kein (15) terms of the available information using kinematics and Newtons equations; 1.2 The natural angular frequency w, and damping factor of the rotating rod if (3) 0 + 25w₁0+w²0= 0 by manipulating the equation of motion if L₁ = 0.400 m. L2 = 0.550 m, L3= 0.720 m, L₁= 0.630 m, Ls = 0.420 m, k₁= 800 N/m, k3= 2450 N/m, c₁ = 450 Ns/m, b = 0.065 m, w = 0.037 m, and 0o = 22° respectively. Total Marks: [18] 3 MOM3602 6 June 2022 Supplied Applicable Formulae for Question 1 I₁ = 1/2m(b² + Iy +w²) I|| = Icom +md² 1 më+ci+kr = 0 + #+25w₁t+w²x = 0,w₂₁ m 6 W B k с .S = m 2mWn << 1 ⇒ r = C[exp(-Cwt)] [sin (wat +)], w₁ = w₁ √/1-(² v=[Cw₁ cos(wat +)-(Cw, sin(wat + x)] e-swit