(b)Figure Q2 shows a system composed of a rod of inertia I, free to rotate aboutthe hinge at point O and supported by a spring of stiffness 3k. The hinge hastorsional stiffness kr. A mass, m, is attached to the free end of the rod by aspring of stiffness 2k and restrained by another spring with stiffness k, asillustrated in Figure Q2.i)ii)Assuming small angular displacements 0, show that the equations ofmotion for this system are1,0 + (11ka² + kŢ)0 - 4kax = 0mx + 3kx - 4ka0 = 0Given 1, = 8 kgm², kr = 200Nm/rad, k = 400 Nm-¹, a = 0.5 m,m = 5 kg, assuming the motion is sinusoidal in both degrees offreedom, calculate the natural frequencies of the system.0www3kFigure Q20Ţm2k

Given : To find : Equations of motion

Figure Q2 shows a system composed of a rod of inertia I, free to rotate about the hinge at point O and supported by a spring of stiffness 3k. The hinge has torsional stiffness kr. A mass, m, is attached to the free end of the rod by a spring of stiffness 2k and restrained by another spring with stiffness k, as illustrated in Figure Q2. Assuming small angular displacements 0, show that the equations of motion for this system are 1,0 + (11ka² + kr)0 - 4kax = 0 mx + 3kx - 4ka0 = 0 ii) Given I, = 8 kgm², k = 200Nm/rad, k = 400 Nm-¹, a = 0.5 m, m = 5 kg, assuming the motion is sinusoidal in both degrees of freedom, calculate the natural frequencies of the system. i) a www 3k Figure Q2 0 Ţ MY m ww 2k

Figure Q2 shows a system composed of a rod of inertia I, free to rotate about the hinge at point O and supported by a spring of stiffness 3k. The hinge has torsional stiffness kr. A mass, m, is attached to the free end of the rod by a spring of stiffness 2k and restrained by another spring with stiffness k, as illustrated in Figure Q2. Assuming small angular displacements 0, show that the equations of motion for this system are 1,0 + (11ka² + kr)0 - 4kax = 0 mx + 3kx - 4ka0 = 0 ii) Given I, = 8 kgm², k = 200Nm/rad, k = 400 Nm-¹, a = 0.5 m, m = 5 kg, assuming the motion is sinusoidal in both degrees of freedom, calculate the natural frequencies of the system. i) a www 3k Figure Q2 0 Ţ MY m ww 2k

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter5: Three-dimensional Equilibrium

Section: Chapter Questions

Problem 5.15P: In Sample Problem 5.5, determine Oy with one scalar equilibrium equation.

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