Sol Q2(10 Marks): An air compressor of weight 981 N is mounted on an elastic foundation. It hasbeen observed that when a harmonic force of amplitude 100 N is applied to the compressor,the steady-state displacement of 5 mm occurs at a frequency of 300 rpm. The compressor isthen modified to include a damping element in the foundation with a damping coefficient of905 N.s/m. Determine (a) the equivalent stiffness (b) the steady state displacement of thefoundation that would limit the 400 rpm, (c) the force transmitted to the foundation.

Answered: Image /qna-images/answer/7a22e0b0-b9b3-4cd0-b51d-e7af98e223b9.jpg

Answered: Q2(10 Marks): An air compressor of…

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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Vipretion
A vehicle weighing 5,000 lb is supported on four identical springs and four identical viscous dampers. The static deflection of the vehicle under its own weight is 10 in. Determine the damping required for each of the dampers so that the critical damping is achieved.
(a) Determine the damping ratio; (b) State whether the system is underdamped, critically damped, or overdamped; (c) Determine x(t) or θ(t) for the given initial conditions
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?
An oscillator system without damping has a natural frequency of omega 0 = pi rad/s. Several types of attenuation are given to the system to provide a damping factor (y) of 0.1, 0.5 and 1 s^-1. (a) For each damping factor value, determine the omega value of the oscillator!. (b) determine the displacement at time t = 2 seconds for the damping factor y = 0.5 , if the displacement at t = O is 30 mm and v = 1.5 m/s
Q1. A single Degree of freedom vibration system has spring stiffness of 7613.3 N/m, mass of 52 kg and critical damping of 1.26x10^3 N.s/m. If the initial velocity for the system is 2 m/s. Determine the displacement and velocity for the system after 2 second.
Q1. The natural frequency of vibration of a person is found to be 5.2 Hz while standing on a horizontal floor. Assuming damping to be negligible, determine the following: a. If the weight of the person is 70 kgf, determine the equivalent stiffness of his body in the vertical direction. b. If the floor is subjected to a vertical harmonic vibration of frequency of 5.3 Hz and amplitude of 0.1 m due to an unbalanced rotating machine operating on the floor, determine the vertical displacement of the person.
The amplitude of vibration of a single degree of freedom spring-mass-damper system is observed to reduce to 15 % of its initial value after 5 cycles. Spring stiffness equals (1500 + 007) N/m and mass equals (7.5 + 007) kg. Determine: The undamped natural frequency; The damped natural frequency; The logarithmic decrement; The damping ratio; and The coefficient of damping.
The natural frequency of an undamped vibrating system is 100 rad/s. A damper with a damping factor of 0.8 is introduced into the system. What is the frequency of vibration of the damped system in rad/s?
Q2: A machine of mass (m) 25.0 kg is placed on an elastic foundation as shown in Figure below. A sinusoidal force of magnitude (F. 25 N) is applied to the machine. A frequency sweep reveals that the maximum steady-state amplitude of 1.3 mm occurs when the period of response is 0.22 s. Determine the equivalent stiffness (K) and damping ratio (E) of the foundation. F sin wt x(t)
A mass of 5 kg is suspended on a spring and set on oscillations. It is observed that theamplitude reduces to 5% of its initial value after 2 oscillations. It takes 0.5 seconds to do thetwo oscillations. Calculate the following.(i) The damping ratio(ii) The natural frequency(iii) The actual frequency(iv) The spring stiffness(v) The critical damping coefficient(vi) The actual damping coefficient
A compact object with a mass of 8.80 kg oscillates at the end of a vertical spring with a spring constant of 1.60 ✕ 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N · s/m. (a) What is the frequency (in Hz) of the damped oscillation? Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value? s (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N · s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? Hz What is the percentage decrease in amplitude in each cycle? % What is the time interval (in s) for the energy to drop to 5.00% of its initial value? s

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