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 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.

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: A machine of mass 203.5 kg is mounted on four parallel springs each of stiffness 1.6 x 105 N/m. When…

Q: Two mass placed on top of each other have a mass of 20 g each and there is a coefficient of static…

A: At the position of amplitude the restoring spring force will be F=kAand therefore the acceleration…

Q: A precision grinding machine is supported on an isolator that has a stiffness of 3 MN/m and a…

Q: A machine of mass 170.8 kg is mounted on four parallel springs each of stiffness 2.2 x 105 N/m. When…

A: The given values are - m =170.8 kg , k = 2.2x105 N/m , f=57.5 Hz , A = 1.4 mm It is also given that…

Q: Engineers can determine properties of a structure that is modeled as a damped spring oscillator,…

A: Given data: The mass of the oscillator is m=0.295 kg The frequency of the oscillator is f=22.6 Hz…

Q: Question 2: A sensitive instrument of mass 100 kg is installed at a location that is subjected to…

A: INTRODUCTION : In this problem, a sensitive device with certain features is used to measure the…

Q: The period Ta of damped linear oscillation for a certain 0.9 kg mass is 0.25 s. If the stiffness of…

Q: QUESTION 2 A vibrating system can be modeled with a mass weighs 20 kg and supported on springs and…

A: The objective of the question is to determine the displacement of a vibrating system after 1 second…

Q: For a certain mass-spring system m = 100 kg and k = 8000 N/m. Determine the value of the critical…

Q: A 2-kg mass is attached to a spring with stiffness 10 N/m. The damping constant for the system is…

A: The mass of block is The spring constant is .The damping constant is .The initial displacement is…

Q: Find the damping coefficient c for this system.

A: Given: m= 24 kg k= 3000 N/m no of cycles (N)=5 xNx0=110x: Amplitude To find: Damping coefficient c…

Q: Two springs, damper and a mass are attached to a rigid, weightless bar PQ as shown below. Write the…

A: The objective of the question is to derive the equation of motion for a system consisting of two…

Q: This problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both…

Q: 1. For the system shown, the spring constant k = 400 kN/m, damping coefficient zeta = 0.5 and the…

Q: 6/20 The force P is applied to (a) the 60-lb block and (b) the 100-lb block. For each case,…

Q: 1. For the system shown, the spring constantk = 400 kN/m, damping coefficient zeta = 0.5 and the…

Q: In an effort to miniaturize a mass-spring system, the mass was reduced by eight times, and the…

A: Calculated free oscillations periods of system.

Q: A set of scales consists of an instrumented spring from which the mass of the measured object can be…

A: Initial mass, mi=10 kgFinal mass, mf=10+20=30 kg

Q: For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and…

Q: has a stiff us damping A precision grinding achine is supported on constant of 4 kN-s/m. The floor…

A: The stiffness is k=2 MN/m=2*106 N/m. The viscous damping constant is c=4 kN-s/m=4*103 Ns/m. The…

Q: A mass-spring system of mass m = 0.2 kg and elastic constant k = 5 N/m is immersed in a viscous…

A: Mass, m=0.2 kgElastic constant, k=5 N/mHarmonic force of intentensity, F0=10 NFrequency=ω…

Q: Consider the spring mass system shown in Figure Task 2b. It has a mass, m of 4 kg and the spring…

Q: You are to investigate the vibration properties of the shock absorber system of a 2000 kg car. The…

A: Given: Mass of the car: →m=2000 Kg So mass of the car on each wheel will be: →m=M4=20004=500 Kg…

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

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.

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 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

MECHANICAL VIBRATIONS
The natural frequency of a system is determined to be 15 Hz ignoring the effects of damping. Calculate the damped natural frequency of the system assuming a damping ratio of 0.7.
A machine of mass 112.7 kg is mounted on four parallel springs each of stiffness 3.2 x 105 N/m. When the machine operates at 58.0 Hz, the machine's steady state amplitude is measured as 0.5 mm. What is the magnitude of force transmitted to the foundations of the machine at this speed? The damping in the system is negligible. (Express answers to 3sf) Answer: 3.49
a lot of people say this is the answer but some say it is not , please check for me
A machine of mass 203.5 kg is mounted on four parallel springs each of stiffness 1.6 x 105 N/m. When the machine operates at 47.2 Hz, the machine's steady state amplitude is measured as 1.0 mm. What is the magnitude of force transmitted to the foundations of the machine at this speed? The damping in the system is negligible. (Express answers to 3sf) Answer:
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…
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.
A block of mass m hangs from a spring with a spring constant k. The block is initially held so that the spring is unstretched. If the natural circular frequency of the system is 10 radians/sec, how many cycles of vibration will the block experience in five seconds after it is released?
[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 weight attached to a spring of stiffness 3.0 lb/in has a viscous damping device. When the weight is displaced and released, the period of vibration is found to be 1.80 seconds and the ratio of consecutive amplitudes is 4.2 to 1.0. Determine the amplitude and phase angle when a force F-2cos(3t) acts on the system.
When an object with a mass of 5 kg is connected to the end of a spring, the spring extends 10 meters and reaches equilibrium. This spring-mass system is placed in an environment with a damping constant of 5 kilograms/second, and the mass is pulled down √ 3 meters from the equilibrium position and released without initial velocity. Find the function that shows the time-dependent change of the position of the given damped spring-mass system. Determine the period and amplitude of the movement. Determine how many seconds it takes for the system to first pass the maximum position (in the positive or negative direction) and the equilibrium position after t = 0. (gravity = 10 meters/second) Then transform the equation of the mass-spring system into a system of equations and draw a sample orbit by creating the vector field of the system and interpret the shape of this orbit.
A damped SDOF system is subjected to harmonic excitation at a frequency of 132 radians/second. If the mass of the system, m = 10 kg, spring constant k = 2500N/m, and damping constant c = 0.7 kg/s, determine the steady state vibration amplitude. Assume the force amplitude as 250N.