A 500 kg electric motor is mounted on flexible supports causing the supports to deflect downward by 6.37 mm. The supports exert a total damping force equal to 50% of the critical value, the damping being proportional to the velocity of motion. (a) Determine the natural frequency, spring stiffness and damping ratio of the system. (b) (c) When the motor is running at 750 rev/min., a sinusoidally varying out of balance vertical force of magnitude 3 kN is produced. Develop an expression that governs the vertical motion of the motor as a function of time. Calculate the maximum percentage force transmitted to the foundation. Suggest ways, giving appropriate reasons, in which this can be reduced. You may consult if you wish to, the figures 8 below showing variation of amplitude ratio (AR) and transmission ratio (TR) with frequency ratio,

A 500 kg electric motor is mounted on flexible supports causing the supports to deflect downward by 6.37 mm. The supports exert a total damping force equal to 50% of the critical value, the damping being proportional to the velocity of motion. (a) Determine the natural frequency, spring stiffness and damping ratio of the system. (b) (c) When the motor is running at 750 rev/min., a sinusoidally varying out of balance vertical force of magnitude 3 kN is produced. Develop an expression that governs the vertical motion of the motor as a function of time. Calculate the maximum percentage force transmitted to the foundation. Suggest ways, giving appropriate reasons, in which this can be reduced. You may consult if you wish to, the figures 8 below showing variation of amplitude ratio (AR) and transmission ratio (TR) with frequency ratio,

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

See similar textbooks

Similar questions

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…
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.
A 0.450kg mass oscillates at the end of a spring with the stiffness of 250 N/m. Thedamping force is proportional to the velocity –av and a= 8.50 kg/s. what is the frequencyof oscillation? What is the damping constant for a critically damped system?
[6] An instrument panel weighing 30 lb is installed in a vehicle on a flexible mount that has an equivalent stiffness k = 400 lb/in and negligible damping. As a result of engine vibration, the vehicle vibrates with a steady-state amplitude of o.25 in at a frequency of 40 Hz. Determine the steady-state amplitude of vibration of the instrument panel.
A vibratory system consists of a mass 12.5 kg, a spring of stiffness 1000 N/m, and a dashpot with damping coefficient of 15 Ns/m. The value of critical damping of the system is (a) 0.223 Ns/m (b) 17.88 Ns/m (c) 71.4 Ns/m (d) 223.6 Ns/m
An underdamped shock absorber is to be designed for a motor cycle of mass 200 kg(m). When the shock absorber is subjected to an initial vertical velocity due to a road bump, the resulting displacement-time curve is to be as indicated below. Find the necessary stiffness and damping constants of the shock absorber if the damped period of vibration is to be 10 sec(τd) and the amplitude x1is to be reduced to one-eighth in one half cycle. Example is attached
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 + 01) N/m and mass equals (7.5 + 01) kg. Determine: The undamped natural frequency; The damped natural frequency; The logarithmic decrement; The damping ratio; and The coefficient of damping.
An air compressor of mass 125 kg is mounted on an elastic foundation, which can be modelled as a mass supported by spring and damper. It has been observed that, when a harmonic force of amplitude 120 N is applied to the compressor, the maximum steady state displacement of 6 mm occurred at a rotational speed of 350 rpm. Determine 1. The equivalent stiffness of the foundation 2. The equivalent damping of the foundation 3. The magnitude of the transmitted force to the foundation
A machine of 250 kg mass is supported on springs of total stiffness 100 kN/m. Machine has an unbalanced rotating force of 350 N at speed of 3600 rpm. Assuming a damping factor of 0.15, the value of transmissibility ratio is:
A (2 kg) mass attached to a linear elastic spring of stiffness (k = 200 N/m) is released from rest when the spring is stretched (10 cm). If the coefficients of static and kinetic friction between the mass and the surface that moves on are (µs = uk = 0.1), determine the damping constant. m Fig (3)
A 96lb weight stretches a spring 3.2ft in equilibrium. it is attached to a dashspot with damping constant of 18lb-sec/ft. The weight is initially displaced 15 inches below equilibrium and given a downward velocity of 12ft/sec.a. What is the natural frequency of the mass and spring in hertz?b. What is the critical damping coeficient in lb-sec/ft? c. After how many seconds will the mass cross the equilibriun the first time?
DEPARTMENT OF MECHANICAL ENGINEERINGMENG 331 DYNAMICS OF MACHINERY