Q1: Find the system's natural frequency shown in thefigure with references to x. The block moves downward andthe disk has radius r and moment inertia (Jo) rotates aboutthe fixed point. Assume the cable is rigid with negligiblemass.2k☑NE E

Answered: Q1: Find the system's natural frequency…

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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6) For the system shown, assume x-y-z is the inertial frame. If the bar first twists around A about the z-axis by a-70°, then the bar BD spins by 0-30° (shown in the picture). Define the transformation matrix to the Bar frame (B) from the Inertia frame (I) and find the location of C with respect to point O expressed in the inertial frame. (Assume a=0 as shown in the picture). 2 ft r=1 ft. B @=30⁰ 1.5 ft
Find the system's natural frequency shown in the figure with references to x. The block moves downward and the disk has radius r and moment inertia (J.) rotates about the fixed point. Assume the cable is rigid with negligible mass. 24 ww Keg 23kme zm
Figure Q4 shows a torsional system consisting of two discs mounted on a shaft with rotational spring stiffnesses k and k2. The two discs have mass moment of inertia J1 and J2. Write down the two equations of motion of the torsional system and determine the frequency equation. (a) (8 If ku = k, kı2 = 2k, Ji = J, J2 = 2J, J = 2000 kg-m², k = 981 kN-m/rad, determine the system's two natural frequencies and corresponding mode shapes. (b) (- k2 Figure Q4
Find the equation of motion for the the figure. one-degree-of-freedom system shown in Find the equilibrium positions of this system and linearize the system about two of its equilibrium positions. Write the linear equations in their simplest possible form: MË + Kε = 0. h fring m 0 L
4. A student followed strictly correct procedure in the lab during the experiment of moment of inertia. He measured the mass and diameter of plastic cylinder with value of m = 0.36 kg and D = 0.1 m. The period of system without plastic cylinder is To = 0.667 s. The period of system with plastic cylinder T₁ = 0.92 s. Find: The spring constant K of the system. If a metallic cylinder and a plastic cylinder have same diameter and same thickness, which one has larger moment of inertia? Explain.
For the traditional AC configurations prove that for the moment of inertia tensor we have Ixy = = yoe²= Iyz = 1 ₁₂y= I 0
Question 1 A sketch of a valve and rocker arm system for an internal combustion engine is give in below figure. Model the system as a pendulum attached to a spring and a mass. Determine the equations of motion and calculate the natural frequency in rad/s. The mass moment of inertia of the rocker arm about its pivot point j=0.46, the stiffness of the valve springspring k=420 , the distance from pivot to spring I= 0.98 m, and the mass of the valve m=3.2 kg. Ignore the mass of the spring and the oil effect. Rocker arm Follower k Valve spring LOil Cam m Valve
DI 4.5-8. Consider the following problem. Мaximize Z = 50x1 + 25x2 + 20x3 + 40x4, subject to 2х + х2 30 X3 + 2x4 < 20
Find the natural frequencies and modal vectors of the system shown in the next figure with m₁ = m, m2 = 2m, k₁ = k, and k₂ = 2k where m = 20 kg and k = 1000 N/m. Note that the equation of motions of the system can be written as m₁x₁ + (k₁ + k₂)x₁ - k2x2 = 0 - m2x2 + k2x2 − k₂x₁ = 0 k₁ Base k2 m1 x₁(t) 00000 m2 x2(1)
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International Edition---engineering Mechanics: St…

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Andrew Pytel And Jaan Kiusalaas

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