EBK SYSTEM DYNAMICS
3rd Edition
ISBN: 8220100254963
Author: Palm
Publisher: MCG
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Chapter 13, Problem 13.3P
A certain factory contains a heavy rotating machine that causes the factory floor to vibrate. We want to operate another piece of equipment nearby and we measure the amplitude of the floor's motion at that point to be 0.01 m. The mass of the equipment is 1500 kg and its support has a stiffness of k = 2x 104 N/m and a damping ratio of < = 0.04. Calculate the maximum force that will be transmitted to the equipment at resonance.
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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 13 Solutions
EBK SYSTEM DYNAMICS
Ch. 13 - Prob. 13.1PCh. 13 - A quarter-car representation of a certain car has...Ch. 13 - A certain factory contains a heavy rotating...Ch. 13 - Prob. 13.4PCh. 13 - Prob. 13.5PCh. 13 - Prob. 13.6PCh. 13 - Prob. 13.7PCh. 13 - Prob. 13.8PCh. 13 - Prob. 13.9PCh. 13 - Alternating-current motors are often designed to...
Ch. 13 - Prob. 13.11PCh. 13 - Prob. 13.12PCh. 13 - Prob. 13.13PCh. 13 - Prob. 13.14PCh. 13 - Prob. 13.15PCh. 13 - Prob. 13.16PCh. 13 - Prob. 13.17PCh. 13 - Prob. 13.18PCh. 13 - Prob. 13.19PCh. 13 - Prob. 13.20PCh. 13 - Prob. 13.21PCh. 13 - Prob. 13.22PCh. 13 - Prob. 13.23PCh. 13 - Prob. 13.24PCh. 13 - Prob. 13.25PCh. 13 - Prob. 13.26PCh. 13 - Prob. 13.27PCh. 13 - Prob. 13.28PCh. 13 - Prob. 13.29PCh. 13 - Prob. 13.30PCh. 13 - Prob. 13.31PCh. 13 - Prob. 13.32PCh. 13 - Prob. 13.33PCh. 13 - Prob. 13.34PCh. 13 - Prob. 13.35P
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