Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY
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Chapter 8.3, Problem 60P
To determine
The frequency range of the base vibration.
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Problem 1 (30 Points)
Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In
scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no
friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in
both scenarios, there is one generalized coordinate, .
R
Scenario 1
R
m
R
g
Scenario 2
m
HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the
bowl (scenario 1), or the pivot point of the pendulum (scenario 2).
Part I
a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points)
b) What can you say about the systems based on the Lagrangian? (2 points)
c) Solve for the equations of motion for both systems. (8 points)
Part II
Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to
determine the normal force acting on the mass.
a)…
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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