29. A lathe machine can be modeled as an electric motor mounted on a steel table. The table plus the motor have a mass of 50 Kg. The rotating parts of the lathe have an out-of-balance mass of 5 kg at a distance 0.1 m form the center. The damping ratio of the system is measured to be 0.06 (viscous damping) and its natural frequency is 7.5 Hz. Calculate the for the following conditions: [Fall 2016-Final] a. Amplitude of the steady state displacement of the motor when or = 30 Hz b. Amplitude of the steady state displacement of the motor at resonance.

29. A lathe machine can be modeled as an electric motor mounted on a steel table. The table plus the motor have a mass of 50 Kg. The rotating parts of the lathe have an out-of-balance mass of 5 kg at a distance 0.1 m form the center. The damping ratio of the system is measured to be 0.06 (viscous damping) and its natural frequency is 7.5 Hz. Calculate the for the following conditions: [Fall 2016-Final] a. Amplitude of the steady state displacement of the motor when or = 30 Hz b. Amplitude of the steady state displacement of the motor at resonance.

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

Related questions

Q: 3. Calculate the natural frequency and damping ratio for the system in figure below. Assume that no…

A: Natural frequency = 40.25 rad/sDamping ratio= 0.00158 System is underdampedExplanation:Step 1:…

Q: Q1:The motion of the simple pendulum can be approximated by the simple harmonic motion (S! or small…

A: from excel spreadsheet we obtain the graph of T2 vs length l.and also obtain the equation for the…

Q: eads damping force g force leads inertia and damping force are rce leads them by 90

Q: 5. For a simple seismograph as shown in Figure Q5 below, the co-ordinate X₁ measures horizontal…

A: Here, The mass m=1 kg. The spring stiffness k=10 Nm-1. The coefficient of the damper, c=2Nsm-1.…

Q: A mass of 7.9 kg oscillates at the end of a spring of stiffness 26.1 Nm¹. If the damping ratio is…

Q: A machine of mass m is mounted on a vibration isolator as shown in Figure 1. Its transfer unction…

A: 8×s+5s2+10s+16s+40×0.05s2+5 X(s) given Plot of response-

Q: 3. A 60-gram mass vibrates in simple harmonic motion (SHM) at the end of a spring. The amplitude of…

Q: uestion - YOur objective is to design a vibration absorber (k2,m2) for the following stem. The…

A: the allowable clearance for the absorber motion =0.01 m20 N amplitude =10 rad/s asiming you can…

Q: A force of 20 newton stretches a spring 1 meter. A 5 kg mass is attached to the spring, and the…

A: Force required to strech a spring F = 20 N Spring streched ∆x = 0.1 m To find Energy does the…

Q: A resistive force is applied to the same mechanical system above, and the amplitude of oscillations…

A: Equation of the motion of a damped harmonic oscillator:The general solution of the above equation.…

Q: 2.- Determine if the system shown (modulator) is: (1 point) 2.1- Linear 2.2. Invariant in time.

Concept explainers

Free Damped Vibrations

Free vibration is a type of vibration in which the external force is removed after giving the initial displacement to a body/system. In other words, in this type of vibration, force is applied at the initial displacement of the system, and after the initial displacement, force is removed, and the system vibrates at the natural frequency.

Question

29. A lathe machine can be modeled as an electric motor mounted on a steel table. The table
plus the motor have a mass of 50 Kg. The rotating parts of the lathe have an out-of-balance
mass of 5 kg at a distance 0.1 m form the center. The damping ratio of the system is measured
to be 0.06 (viscous damping) and its natural frequency is 7.5 Hz. Calculate the for the
following conditions:
[Fall 2016-Final]
Amplitude of the steady state displacement of the motor when or = 30 Hz
Amplitude of the steady state displacement of the motor at resonance.
Determine the force transmitted to the foundation, at resonance, due to maximum
a.
b.
C.
displacement.
d. Determine the force transmitted to the foundation, at resonance, due to maximum
velocity.
Hint:
- at maximum displacement, the velocity is zero.
- at the maximum velocity, the displacement is zero.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: step 1

VIEW

Step 2: step 2

VIEW

Solution

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

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

A mass of 10kg oscillates at the end of a spring of stiffness, 5N/m. If the damping in the system is such that it gives a damping ratio of 0.45, determine. i) The critical damping. ii) The value of the damping coefficient. iii) The damped natural frequency. iv) The equation for the displacement if the initial velocity is 0.025m/s, and the initial displacement is 0 m.
Can you please show the complete solution of the image below. Thanks! Subject: Mechanical Vibration
A pump of mass 30 kg is supported on a support structure which has 4 springsarranged in parallel with stiffness values of 10 kN/m, 15 kN/m, 8 kN/m and12 kN/m respectively. Viscous damping is present within the system and 1 kNs/mis applied by a damper.i) Produce a neat sketch of the system and state its equation of motion.ii) Determine the damping ratio for the system, commenting on its value. iii) Determine the damped frequency of vibration.iv) Determine the logarithmic decrement for the vibrating system.
Suppose we have determined that the lowest natural frequency of a particular helical compression spring is 20286 rpm. According to the prescription in our book and according to the presentation in class, find the highest recommended operating frequency of a machine that utilizes this spring. Give your answer in rpm, but do not include units--Blackboard will not understand
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…
Title Plot the solution of a linear, spring and mass system with frequency ?n = 3 rad/s, x0 = 1.2mm and v0 Description Plot the solution of a linear, spring and mass system with frequency ωn = 3 rad/s, x0 = 1.2mm and v0 = 2.34mm/s, for at least two periods. Compute the natural frequency and plot the solution of a spring-mass system with mass of 2 kg and stiffness of 4 N/m, and initial conditions of x0 = 1mm and v0 = 0mm/s, for at least two periods.
Given an oscillator of mass 2.0kg and spring constant of 180N/m, what is the period without damping? Use numerical methods to model this oscillator with an additional friction force equal to where c is a positive damping constant. Using c=5.0, what is the new period of oscillation. What about for c=10? Assume initial position is 0.2m and initial velocity is zero. Please find the period using the position versus time plot and use the first full cycle of the motion.
2. Calculate the natural frequency and damping ratio for the system in figure below given the values m = 10 kg, c = 100 kg/s, k₁ 4000 N/m, k2 200 N/m, and k3 1000 N/m. = Assume that no friction acts on the rollers. Is the system overdamped, critically damped, or underdamped? C кий m k₂ k3
A mass-spring damper system has the following parameters: • mass 250g damping constant 1/36000 Nh/m • spring stiffness 500 N/m Calculate the damped frequency. O 1.55.2 rad/s O 2.25.8 rad/s O 3. Not possible to calculate. O 4.79.4 rad/s O 5.44.7 rad/s
QI: A portion of an automobile suspension system consists of an elastic spring and a viscous damper, as shown. If the natural frequency is 10 rad/sec, a) Determine the damping ratio so that any oscillations that occur will decay from 11-0.5 m to x2-D 0.025 m. b) If the system is displaced 0.2 m from its equilibrium position, and released from rest, determine the position of the mass after it has ascillated through 3 cycles.