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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The measurements on a mechanical vibrating system show that it has a mass of 8 kg and that the springs can be combined to give an equivalent spring of stiffness 5.4 N/mm. If the vibrating system have a dashpot attached which exerts a force of 40 N when the mass has a velocity of 1 m/s, find : 1. critical damping coefficient, 2. damping factor, 3. logarithmic decrement, and 4. ratio of two consecutive amplitudes.
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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- Please answer with explanation. I will really upvotearrow_forwardA single degree of freedom mass-spring-damper system is subject to vibration under the influence of a harmonic force. On my site, it is given as m=2 kg, k=800 N/m, c=64 Ns/m. The amplitude of the harmonic force is F0=256 N and its frequency is w= 20 rad/s. Answer the questions in options a, b, and c according to the given information. 1) Calculate the damping ratio of the system (ξ) a.1 b.0.7 c.0.9 d.0.8 2)Calculate the magnification factor (M) of the system. a.0.86 b.1.25 c.0.312 D.0.625 3-) Calculate the maximum vibration amplitude (X) (meters). a.0.2 b.0.1 c.0.4 D.0.3arrow_forwardHello, please solve this problem. Thank you very mucharrow_forward
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- 4. Find the equivalent damping constant for this mechanical system in terms of its parameters ( k, c, m1, m2, 0). ma Hilind m1arrow_forwardA 19 kg object is attached to a spring with spring constant 16 kg/s2. It is also attached to a dashpot with damping constant c = object is initially displaced 5 m above equilibrium and released. Find its displacement and time-varying amplitude for t > 0. 7 N-sec/m. The y(t) e-0.184t (5 cos (0.9t) + sin(0.9t)) The motion in this example is O critically damped O overdamped O underdamped Consider the same setup above, but now suppose the object is under the influence of an outside force given by F(t) 4 cos(wt). What value for w will produce the maximum possible amplitude for the steady state component of the solution? 0.977 What is the maximum possible amplitude? 2.30arrow_forwardIn a damped single-degree-of-freedom system with a mass of m = 10 kg, stiffness coefficient k = 4000 N/m, and damping coefficient c = 40 Ns/m, the excitation force's amplitude is Fo 60 N, and its natural angular frequency is wf = 40 rad/s. Determine the forced vibration amplitude and phase angle. =arrow_forward
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Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license