A 110 kg machine is mounted on an elastic foundation of stiffness 2×106 N/m. When operatingat 150 rad/s, the machine is subjected to a harmonic force of magnitude 1500 N. The steadystate amplitude of the machine is measured as 1.9 mm.Find•the frequency ratiothe amplitude ratio or the magnification factorWhat is the damping ratio of the foundation?

Calculated frequency ratio and magnification factor and damping ratio of the foundation.

Answered: A 110 kg machine is mounted on an…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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A 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.
1) A 45 kg machine is mounted on four parallel springs each of stiffness 2x10^5 N/m and a damping ratio of 0.1. When the machine operates at 32 Hz the machine's steady-state amplitude is measured as 1.5 mm. What is the magnitude of the excitation provided to the machine at this speed?
A 10 kg vibrating system is placed on a table which is bolted to the floor. Due to operation of rotating equipment, the floor has a vibration amplitude of 0.2 mm at a frequency of 30 Hz. If the table is modeled as a spring of stiffness 1.3x106 N/m with a damping ratio of 0.04. Find the steady state acceleration amplitude of the vibrating system.
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 machine weighing 300lb is mounted on a supporting system consisting of four springs and four dampers. The vertical deflection of the supporting system under the weight of the machine is measured as 0.75in. The dampers are designed to reduce the amplitudeof vertical vibration to one-sixthof the initial amplitude after two complete cycles of free vibration. Find the following undamped natural frequency,damping ratio, and damped natural frequencyofthesystem.
A 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.0.3
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An industrial sewing machine of 65 kg has an unbalance value of 0.15 kgm per rotation. The machine operates at 125 Hz and is located on the ground with a spring coefficient of 2 x 106N / m and a dimensionless damping coefficient of 0.12. Find the uniform regime amplitude of the machine.
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 car
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