System Dynamics
3rd Edition
ISBN: 9780077509125
Author: Palm
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
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.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
The figure below shows a simple model of a motor vehicle that can vibrate in the vertical direction while traveling over a rough road. The vehicle has a mass of 1200 kg. The suspension system has a spring constant of 400 kN/m and a damping ratio of ζ = 0.5. If the vehicle speed is 20 km/hr, determine the displacement amplitude of the vehicle. The road surface varies sinusoidally with an amplitude of Y=0.05m and a wavelength of 6 m.
(please use the second images' conditions to answer the question above)
(Also, please submit screenshot of matlab)
A heavy machine, weighing 3000 N, is supported on a resilient foundation. The static deflection of the foundation due to the weight of the machine is found to be 7.5 cm. It is observed that the machine vibrates with an amplitude of 1 cm when the base of the foundation is subjected to harmonic oscillation at the undamped natural frequency of the system with an amplitude of 0.25 cm. Find
a. the damping constant of the foundation,
b. the dynamic force amplitude on the base, and
c. the amplitude of the displacement of the machine relative to the base.
: A spring-mass system is excited by a force F sin wt. At resonance the amplitude is measured to be 0.62cm. At 0.85 resonant frequency, the amplitude is measured to be 0.48cm. Determine the damping factor of the system.
Chapter 13 Solutions
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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Similar questions
- An automobile whose weight is 150 N and it is mounted on 4 identical springs due to its weight it sags by 250 mm . each shock absorber has damping coefficient of 0.4 N for a velocity oof 30 mm/sec. The car is placed on a platform which moves vertically at resonance speed having an amplitude of 10mm. Find the amplitude of the cararrow_forwardA machine, weighing 3000 N, is supported on a resilient foundation. The static deflection ofthe foundation due to the weight is 7.5 cm. It is observed that the machine vibrates with anamplitude of 1 cm when the base of the foundation is subject to harmonic oscillation at theundamped natural frequency of the system with an amplitude of 0.25 cm. Find(a) the damping constant of the foundation;(b) the maximum force transmitted to the base;(c) the amplitude of the displacement of the machine relative to the base.arrow_forwardA 65 kg painted sewing machine has an imbalance value of 0.15 kgm in rotation. The machine operates at 125 Hz and is located on the ground with a spring coefficient of 2 x 106 N / m and a dimensionless attenuation coefficient of 0.12. Find the uniform regime amplitude of the machine.arrow_forward
- A reciprocating machine weighing 100kN is known to develop vertically oriented harmonic forces having and amplitude of 2.5kN at its operating speed of 40Hz. In order to limit the vibrations excited in the building in which the machine is installed, it is to be supported by a spring at each corner of its rectangular base. The designer wants to know what support spring stiffness would be required to limit to 0.4kN, the total harmonic force transmitted from the machine to the building.arrow_forwardA radio set of 20 kg mass must be isolated from a machine vibrating with an amplitude of 0.05 mm at 500 cpm. The set is mounted on four isolators, each having a spring scale of 31400 N/m and damping factor of 392 N-sec/m. What is the amplitude of vibration of the radio & dynamic load on each isolator due to vibration?arrow_forwardA 2.50-kg object is attached to a spring with a force constant of 4.50 N/m. The object rests on a horizontal surface that has a viscous, oily substance spread evenly on it. The object is pulled 15.0 cm to the right of the equilibrium position and set into harmonic motion. After ?1=2.00 s the amplitude has fallen to 7.00 cm due to frictional losses in the oil. Calculate the damping constant ? for the oil.arrow_forward
- An air compressor, weighing 100 kg, is mounted on an elastic foundation. I knowhas observed that when a harmonic force of 150 N amplitude is applied to the compressor, theMaximum steady state displacement is 6.2mm and occurs at a frequency of 320rpm.Determine: a) the equivalent stiffness, b) the damping constant "C" of the foundation andc) The force transmitted to the foundation. d) Illustrate using graphicsarrow_forwardA block of mass m = 16 kg oscillates attached to a spring of spring constant K = 162 N/m. The motion of the block is also acted upon by a damping force proportional to the velocity of the form Fd = -bv, where b = 36√ 2 kg/s. The system is excited by a sinusoidal force of maximum value F0 = 7 N. If the excitation frequency varies, at what frequency ω (in rad/s) will resonance occur? Choose the closest value. a) 63/4 rad/s b) 9/28 rad/s c) 567/4 rad/s d) 9/4 rad/sarrow_forwardThe model for free vibrations of the vehicle suspension system with an empty vehicle is 300\dot{x}+1200\dot{x}+12000x=0 Determine the natural frequency f_{n} and damping ratio ζ of the suspension system.arrow_forward
- A precision grinding machine is supported on an isolator that has a stiffness of 3 MN/m and a viscous damping constant of 3 kN-s/m. The floor on which the machine is mounted is subjected to a harmonic disturbance due to the operation of an unbalanced engine in the vicinity of the grinding machine. Find the maximum acceptable displacement amplitude of the floor if the resulting amplitude of vibration of the grinding wheel is to be restricted to 4*10^(-6)m. Assume that the grinding machine and the wheel are a rigid body of weight 6000 N. Use omega=100*Pi (previous answer to the same problem just different numbers)arrow_forwardThe amplitude of the steady-state response of a single-degree-of-freedom device is x=5 mm, when the excitation frequency is Ω=ωn. System mass m=200 kg. Fastening stiffness k=30 kNm and damping ratio ς=0.1. The system is loaded by the force F(t)=e^(i*Ω*t). How much must the excitation frequency be changed in order for the amplitude of the device to decrease to the value x=1 mm?arrow_forwardA spring-mass system with m = 0.5 kg and k = 10,000 N/m with negligible damping, is used as a vibration pickup. When mounted on a structure vibrating with an amplitude of 4 mm, the total displacement of the mass of the pickup is observed to be 12 mm. Find the frequency of the vibrating structure.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY
Ch 2 - 2.2.2 Forced Undamped Oscillation; Author: Benjamin Drew;https://www.youtube.com/watch?v=6Tb7Rx-bCWE;License: Standard youtube license