vibrationsshow all steps and solutions A machine of mass 150 kg supported on springs of equivalent stiffness1000 kN/m has a rotating unbalance force of 6000 N at a speed of 2000 rpm Ifthe damping ratio is 0.2, determine(a) the amplitude caused by the unbalance and its phase angle,(b) the transmissibility ratio and(c) the actual force transmitted.

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Answered: A machine of mass 150 kg supported on…

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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Mohammed Mahad Tabook A lathe can be modeled as an electric motor mounted on a steel table. The table plus rotor have a mass of 100 kg. The rotating parts of the lathe have a mass of 10 kg at a distance 0.1 m from the center. The damping ratio of the system is measured to be zeta= 0.06 (viscous damping) and its natural frequency is 7.5 Hz and the driving frequency is 30HZ The natural frequency in rad/s is Choose.. The driving frequency in rad/s is Choose... The frequency ratio is Choose... The amplitude of the steady-state displacement of the motor (in mm) Choose... the phase shift of the steady state displacement (in rad) is Choose... +
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.
A reciprocating pump of 200 kg is driven through a belt by an electric motor at 3000 rev/min. The pump is mounted on isolators with total stiffness of 5 M N/m and damping of 3.125 kN-s/m. Determine the vibrating amplitude of the pump at the running speed due to fundamental harmonic force of excitation, 1 kN. Also determine the maximum vibratory amplitude when the pump is switched "ON' and the motor speed passes through resonant condition.
A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator. Find the damping ratio of the system ζ . Find the transmissibility of the system, Tf. Find the frequency ratio of the system, β. Find the amplitude of the harmonic excitation force of the system, Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X in millimeters (mm). Find the damped frequency of the system, ωd in rad/s. Find the force transmitted to the foundation, FT in Newton (N). Find the frequency of the harmonic…
A rotating machine of 400 kg is similar to the system shown below. It operates at 3600 rpm (note: 1 rpm = 2π/60 rad/s). The machine is unbalanced such that its effect is equivalent to a 4 kg mass located 20 cm from the axis of rotation. An isolator with a spring stiffness of 8x106 N/m and a damping constant of 2x104 Ns/m is placed between the machine and the foundation. Determine the steady state response of the system. Find the force transmitted to the foundation and transmissibility of the isolator. Find the damping ratio of the system ζ . Find the transmissibility of the system, Tf. Find the frequency ratio of the system, β. Find the amplitude of the harmonic excitation force of the system, Fo in Newton (N). Find the displacement amplitude of the steady state response of the system, X in millimeters (mm). Find the damped frequency of the system, ωd in rad/s. Find the force transmitted to the foundation, FT in Newton (N). Find the frequency of the harmonic…
A 7-kg block is suspended by three identical springs, each with k = 200 N/m. The bottom of the block is attached to a dashpot that provides a damping force of F= 50|M N, where v is in m/s. At t = 0 s, the block is given an initial velocity upward of 0.6 m/s from its equilibrium position. (a) What is the natural frequency of the system? (b) Show whether this is an underdamped, a critically damped, or an overdamped system. (c) What is the frequency of the damped system? (d) What is the amplitude of the damped oscillation?
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A 100-kg compressor rotor has a shaft stiffness of 1.4x 107 N/m. The compressor is designed to operate at a speed of 6000 rpm. The internal damping of the rotor shaft system is measured to be = 0.01. The rotor has an eccentric radius of 10mm.Determine: a) the displacement amplitude, X, at operating speed b) the critical speed ( in rpm) of the rotor system c) the whirl amplitude at critical speed.
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A structure that can be idealized as a SDOF system has a mass 100 kg, a stiffness of 40 kN/m and a damping ratio of 0.10. If it is subjected to a harmonic dynamic force given by p(t) = 500 sin(15 t) N, determine (a) the dynamic amplification under steady-state conditions; (b) the maximum velocity of the steady state vibration; and (c) the maximum amplitude if the forcing frequency was equal to the system frequency (a resonant condition).
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.

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