Question 1 Consider An Inclined Bar Made Of Two Sections Of Length L Connected To A Spring Of Constant K And Length L 1 (140.66 KiB) Viewed 76 times
Question 1 Consider An Inclined Bar Made Of Two Sections Of Length L Connected To A Spring Of Constant K And Length L 2 (27.74 KiB) Viewed 76 times
QUESTION 1 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 kı L₁ 00 m Y 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: d²0 de 1.1 (3) 1.2 The equation of motion of the rotating rod in the form megd? + 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 + 25w₁0 + ²0 = 0 by manipulating the equation of motion if L₁ = 0.400 m, L2 = 0.550 m, L3 = 0.720 m, L4 = 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. = Total Marks: [18] W b Ꮨ .
Supplied Applicable Formulae for Question 1 Iy = 1/2m(b² + w²) I|| = = Icom + md² 3 k с mä +ci+kx = 0 → ï +25w₁x + w ²/x = 0, wn = m 2mwn (<1 ⇒ x = C[exp (-Cwnt)] [sin (wat +)], wa = wn V - (2 = [Cwa cos(wat +) - (Cwn sin(wat + 4)] e=Sunt V=
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