
Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY
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Question
Chapter 8.2, Problem 40P
To determine
The equation of motion, the critical frequency of the system and the damping ratio.
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In MATLAB write out a program to integrate the equations of motion of a rigid body. The inertia matrix is given by I = [125 0 0; 0 100 0; 0 0 75] which is a diagonal, where diag operator provides a matrix with given elements placed on its diagonal. Consider three cases where the body rotates 1 rad/sec about each principal axis. Integrate the resulting motion and study the angular rates and the resulting attitude (use any attitude coordinates). For each principal axis case, assume first that a pure spin about the principal axis is performed, and then repeat the simulation where a small 0.1 rad/sec motion is present about another principal axis. Discuss the stability of each motion. The code should produce a total of 6 simulations results when it is ran.
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Using the Mohr's Strain Circle calculate the:
[10 marks]
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(i) principal strains (1, 2)?
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[5 marks]
(ii) principal angles (1, 2)?
You should measure these anticlockwise from the y-axis.
20
[5 marks]
(iii) maximum shear strain in the plane (ymax)?
Ex = Ea
Ey = εc
[5 marks]
(epol)
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Ea = A = -210
2
B=E₁ = -50
E₁ = C = 340
D = 45°
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1)
Solve and show which is converage or diyverage
a = 2+(0.1)"
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16) a =
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an
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18) a =√4"n
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20) a =
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a₁ =
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a=1+(-1)"
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a
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23) a=
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8) a =
24) a =
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a = sin
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10) an =
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25) a = tanh(n)
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26) a = -sin-
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27) a = tan(n)
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30) an-√n²-1
1
28) a =
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31) a=-
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nix
Chapter 8 Solutions
Engineering Mechanics: Dynamics
Ch. 8.2 - When a 3-kg collar is placed upon the pan which is...Ch. 8.2 - Prob. 2PCh. 8.2 - Prob. 3PCh. 8.2 - For the system of Prob. 8/2, determine the...Ch. 8.2 - Prob. 5PCh. 8.2 - Prob. 6PCh. 8.2 - Prob. 7PCh. 8.2 - The vertical plunger has a mass of 2.5 kg and is...Ch. 8.2 - Determine the period τ for the system shown. The...Ch. 8.2 - Prob. 10P
Ch. 8.2 - Prob. 11PCh. 8.2 - Prob. 12PCh. 8.2 - Prob. 13PCh. 8.2 - Prob. 14PCh. 8.2 - Prob. 15PCh. 8.2 - Calculate the natural frequency fn of vibration if...Ch. 8.2 - Prob. 17PCh. 8.2 - Prob. 18PCh. 8.2 - Prob. 19PCh. 8.2 - Prob. 20PCh. 8.2 - Prob. 21PCh. 8.2 - Prob. 22PCh. 8.2 - Prob. 23PCh. 8.2 - Prob. 24PCh. 8.2 - Prob. 25PCh. 8.2 - Prob. 26PCh. 8.2 - Prob. 27PCh. 8.2 - Prob. 28PCh. 8.2 - Prob. 29PCh. 8.2 - Prob. 30PCh. 8.2 - Prob. 31PCh. 8.2 - Prob. 32PCh. 8.2 - Prob. 33PCh. 8.2 - Prob. 34PCh. 8.2 - Derive the differential equation of motion for the...Ch. 8.2 - Prob. 36PCh. 8.2 - Determine the equation of motion for the system in...Ch. 8.2 - Prob. 38PCh. 8.2 - Prob. 39PCh. 8.2 - Prob. 40PCh. 8.2 - Prob. 41PCh. 8.2 - Prob. 42PCh. 8.2 - Prob. 43PCh. 8.2 - Prob. 44PCh. 8.3 - Prob. 45PCh. 8.3 - Prob. 46PCh. 8.3 - Prob. 47PCh. 8.3 - Prob. 48PCh. 8.3 - Prob. 49PCh. 8.3 - Prob. 50PCh. 8.3 - Prob. 51PCh. 8.3 - Prob. 52PCh. 8.3 - Prob. 53PCh. 8.3 - The 4-lb body is attached to two springs, each of...Ch. 8.3 - Prob. 55PCh. 8.3 - The motion of the outer frame B is given by xB = b...Ch. 8.3 - Prob. 57PCh. 8.3 - Prob. 58PCh. 8.3 - When the person stands in the center of the floor...Ch. 8.3 - Prob. 60PCh. 8.3 - Derive the equation of motion for the inertial...Ch. 8.3 - Prob. 62PCh. 8.3 - Prob. 63PCh. 8.3 - Prob. 64PCh. 8.3 - Prob. 65PCh. 8.3 - Prob. 66PCh. 8.3 - Derive and solve the equation of motion for the...Ch. 8.3 - Prob. 68PCh. 8.3 - Prob. 69PCh. 8.3 - Prob. 70PCh. 8.4 - The light rod and attached small spheres of mass m...Ch. 8.4 - Prob. 72PCh. 8.4 - The thin square plate is suspended from a socket...Ch. 8.4 - Prob. 74PCh. 8.4 - The 20-lb spoked wheel has a centroidal radius of...Ch. 8.4 - Prob. 76PCh. 8.4 - The uniform sector has mass m and is freely hinged...Ch. 8.4 - Prob. 78PCh. 8.4 - Prob. 79PCh. 8.4 - Prob. 80PCh. 8.4 - Prob. 81PCh. 8.4 - Prob. 82PCh. 8.4 - Prob. 83PCh. 8.4 - Prob. 84PCh. 8.4 - Prob. 85PCh. 8.4 - Prob. 86PCh. 8.4 - Prob. 87PCh. 8.4 - Prob. 88PCh. 8.4 - Prob. 89PCh. 8.4 - Prob. 90PCh. 8.4 - Prob. 91PCh. 8.4 - Prob. 92PCh. 8.4 - Prob. 93PCh. 8.4 - Prob. 94PCh. 8.4 - Prob. 95PCh. 8.4 - Prob. 96PCh. 8.5 - The 1.5-kg bar OA is suspended vertically from the...Ch. 8.5 - The light rod and attached sphere of mass m are at...Ch. 8.5 - A uniform rod of mass m and length l is welded at...Ch. 8.5 - The spoked wheel of radius r, mass m, and...Ch. 8.5 - Prob. 101PCh. 8.5 - The length of the spring is adjusted so that the...Ch. 8.5 - The body consists of two slender uniform rods...Ch. 8.5 - By the method of this article, determine the...Ch. 8.5 - Prob. 105PCh. 8.5 - Prob. 106PCh. 8.5 - Prob. 107PCh. 8.5 - Prob. 108PCh. 8.5 - Prob. 109PCh. 8.5 - Prob. 110PCh. 8.5 - Prob. 111PCh. 8.5 - Prob. 112PCh. 8.5 - Prob. 113PCh. 8.5 - Prob. 114PCh. 8.5 - Prob. 115PCh. 8.5 - Prob. 116PCh. 8.5 - Prob. 117PCh. 8.5 - The quarter-circular sector of mass m and radius r...Ch. 8.6 - Prob. 119RPCh. 8.6 - Prob. 120RPCh. 8.6 - Prob. 121RPCh. 8.6 - Prob. 122RPCh. 8.6 - Prob. 123RPCh. 8.6 - Prob. 124RPCh. 8.6 - Prob. 125RPCh. 8.6 - Prob. 126RPCh. 8.6 - Prob. 127RPCh. 8.6 - Prob. 128RPCh. 8.6 - Prob. 129RPCh. 8.6 - Prob. 130RPCh. 8.6 - Prob. 131RPCh. 8.6 - Prob. 132RPCh. 8.6 - Prob. 133RPCh. 8.6 - Prob. 137RPCh. 8.6 - Prob. 138RPCh. 8.6 - Prob. 139RPCh. 8.6 - Prob. 140RP
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