EBK ENGINEERING MECHANICS
15th Edition
ISBN: 9780137616909
Author: HIBBELER
Publisher: VST
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Chapter 22, Problem 55P
To determine
The amplitude of the steady state vibration of the fan.
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See the attached image. Please provide the solution modeled as a differential equation. Include an equation of motion of the mass for both no damping force and a damping resistance equal to half the velocity (please notate and show how to identify the velocity) with detailed steps and explanation of the solution.
Example-3. Determine natural frequency, damped natural frequency, damping ratio and
logarithmic decrement for the system as shown:
21
Neglect mass of rod
m
TWwwx
THEATEFNT
mummi
Consider the double mass/double spring system shown below.
- click to expand.
Both springs have spring constants k, and both masses have mass m; each spring is subject to a damping force of Ffriction -cz' (friction proportional to velocity).
We can write the resulting system of second-order DEs as a first-order system, t' (t) = Au(t), with = (₁, 21, 22, 2₂) I
For values of k = 4, m = 1 and c = 1, the resulting eigenvalues and eigenvectors of A are
-0.039-0.248i
0.813
A₁2=-0.5±3.2i, v₁ =
0.024 +0.153i
-0.502
-0.134-0.302i
0.409
-0.2160.489
0.661
(a) Find a set of initial displacements (0), 2(0) that will lead to the fast mode of oscillation for this sytem. Assume that the initial velocities wil be zero.
A3,4 -0.5± 1.13i, z =
and
(2₁ (0), ₂(0)) =
Enter your answer using angle braces, (and).
(b) At what frequency will the masses be oscillating in this mode?
Frequency
rad/s
Chapter 22 Solutions
EBK ENGINEERING MECHANICS
Ch. 22 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22 - A spring has a stiffness of 800 N/m. If a 2-kg...Ch. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - A 3-kg block is suspended from a spring having a...Ch. 22 - Prob. 10P
Ch. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Prob. 16PCh. 22 - Prob. 17PCh. 22 - A uniform board is supported on two wheels which...Ch. 22 - Prob. 24PCh. 22 - Prob. 30PCh. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Determine the differential equation of motion of...Ch. 22 - Prob. 36PCh. 22 - If the block-and-spring model is subjected to the...Ch. 22 - A block which has a mass m is suspended from a...Ch. 22 - A 4-lb weight is attached to a spring having a...Ch. 22 - A 4-kg block is suspended from a spring that has a...Ch. 22 - A 5-kg block is suspended from a spring having a...Ch. 22 - Prob. 48PCh. 22 - The light elastic rod supports a 4-kg sphere. When...Ch. 22 - Find the differential equation for small...Ch. 22 - Prob. 52PCh. 22 - The fan has a mass of 25 kg and is fixed to the...Ch. 22 - In Prob. 22-53 , determine the amplitude of...Ch. 22 - Prob. 55PCh. 22 - Prob. 56PCh. 22 - Prob. 57PCh. 22 - Prob. 58PCh. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 61PCh. 22 - Prob. 62PCh. 22 - Prob. 65PCh. 22 - Determine the magnification factor of the block,...Ch. 22 - Prob. 67PCh. 22 - The 200-lb electric motor is fastened to the...Ch. 22 - Prob. 70PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 79P
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