PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 22, Problem 76P
To determine
The differential equation of motion for the damped vibratory system and the type of motion.
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Determine the differential equation of
motion for the damped free vibratory
system shown. What type of motion occurs?
Take k=100 N/m, c = 200 N.s/m and m=25
kg
O
25y + 300y = 0 and it is ur
ÿ +12y + 16y = 0 and it is
25y + 300y + 400y = 0 and
ÿ + 16y + 12y = 0 and it is
A SDOF system with a mass 25 kg and stiffness 10 N/mm with damping 0.15 Ns/m is initially at rest. IF the inital velocity is 100 mm/sec. find the expression for subsequent displacement .Hence find displacement and velocity at t=2 secs
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?
Chapter 22 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 22 - A spring is stretched 175 mm by an 8-kg block. If...Ch. 22 - A spring has a stiffness of 800 N/m. If a 2-kg...Ch. 22 - Prob. 3PCh. 22 - Prob. 4PCh. 22 - Prob. 5PCh. 22 - Prob. 6PCh. 22 - Prob. 7PCh. 22 - Prob. 8PCh. 22 - A 3-kg block is suspended from a spring having a...Ch. 22 - Prob. 10P
Ch. 22 - Prob. 13PCh. 22 - Prob. 14PCh. 22 - Prob. 16PCh. 22 - Prob. 17PCh. 22 - A uniform board is supported on two wheels which...Ch. 22 - Prob. 24PCh. 22 - Prob. 30PCh. 22 - Prob. 31PCh. 22 - Prob. 32PCh. 22 - Determine the differential equation of motion of...Ch. 22 - Prob. 36PCh. 22 - If the block-and-spring model is subjected to the...Ch. 22 - A block which has a mass m is suspended from a...Ch. 22 - A 4-lb weight is attached to a spring having a...Ch. 22 - A 4-kg block is suspended from a spring that has a...Ch. 22 - A 5-kg block is suspended from a spring having a...Ch. 22 - Prob. 48PCh. 22 - The light elastic rod supports a 4-kg sphere. When...Ch. 22 - Find the differential equation for small...Ch. 22 - Prob. 52PCh. 22 - The fan has a mass of 25 kg and is fixed to the...Ch. 22 - In Prob. 22-53 , determine the amplitude of...Ch. 22 - Prob. 55PCh. 22 - Prob. 56PCh. 22 - Prob. 57PCh. 22 - Prob. 58PCh. 22 - Prob. 59PCh. 22 - Prob. 60PCh. 22 - Prob. 61PCh. 22 - Prob. 62PCh. 22 - Prob. 65PCh. 22 - Determine the magnification factor of the block,...Ch. 22 - Prob. 67PCh. 22 - The 200-lb electric motor is fastened to the...Ch. 22 - Prob. 70PCh. 22 - Prob. 72PCh. 22 - Prob. 73PCh. 22 - Prob. 74PCh. 22 - Prob. 75PCh. 22 - Prob. 76PCh. 22 - Prob. 79P
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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 vertical spring-mass system is submerged in oil. The spring has a stiffness coefficient of 3 N/m, and the mass is 1 kg. If the dampened angular frequency omega_d of oscillation is 0.866 Hz, find the damping coefficient b for the oil and how long it takes the spring to reach 50 percent of its original amplitude.arrow_forwardProblem 6: An object of mass 2 kg is attached to a spring of stiffness 200 N/m on a horizontal frictionless surface. Then it is extending by 10 cm and then let free to oscillate. 1- How long will it take to make one complete oscillation? 2- Determine the amplitude and give an expression for the displacement as a function of time. 3- Calculate its displacement, velocity, acceleration and force acting on it after sec. 4- Calculate its velocity by the time it is extended by 0.5 cm.arrow_forwardDamped Oscillatory Motion The setup consists of a mass m and a mass ", connected by a massless string of length { via a massless pulley. There is no friction between the string and the pulley. Mass m/2 is connected to a spring (spring constant k) and to a damper, damping constant b. Write down the equation of motion for the mass m. Use the coordinate x, with x = 0 being the equilibrium position of the system. Question т m/2] k barrow_forward
- Q1) A vibratory system with viscous damping: Mass = 1 kg; spring constant k = 25 N/m. The mass is given an initial velocity of vo= 20 m/s from rest position. Find the equation of motion and the displacement of the mass after two second if the damping coefficient is 20 N/m/s, +arrow_forwardConsider a spring-mass system with mass equal to 1 kg, spring constant equal to 25 Newton/meter.Which damping constant b causes critical damping?If the damping constant b in the above system is set to 3 N ∙ sec/m, then what can be said about the number of timesdoes the object pass through its equilibrium position?If the damping constant b in the above system is set to 8 N ∙ sec/m, then what is the interval of time between thesecond time the object returns to its equilibrium position and the third time it returns to its equilibrium position?arrow_forwardi. À. vehicle wheel, tire, and suspension can be modeled as a SDOF spring nd mass as depicted below: The mass of the wheel and tire is measured to be 300 kg and its frequency of oscillation is observed to be 10 rad/sec. What is he stiffness of the wheel assembly? vehicle frame suspension tire and wheelarrow_forward
- Question 2: A sensitive instrument of mass 100 kg is installed at a location that is subjected to harmonic motion with frequency 20 Hz and acceleration 0.5 m/s². If the instrument is supported on an isolator having a stiffness k = 25x10ª N/m and a damping ratio č = 0.05, determine the maximum acceleration experienced by the instrument. %3Darrow_forwardFor the shown spring-mass-damper system. Let m =1 kg, b = 2 N.s/m, k = 2 N/m and f(t) = sin2t N. (a) Write the equation of motion. (b) Find the amplitude of the steady state oscillations. (c) Find the steady state maximum acceleration.arrow_forward3. A 100-pound weight is suspended from a vertical spring whose module is 100 pounds per foot. The weight is pulled downward 9 inches from its equilibrium position and released. Viscous fluid exerts 20 Ibs of force when the plunger moves through it at 0.5 ft/sec; 3.a What is the damping condition? Write the equation which describes the motion of the weights. Show graph. 3.b displacement 3.c velocity 3.d accelerationarrow_forward
- For the mechanical system shown, a- Find the equivalent mass, equivalent spring stiffness and equivalent damping coefficient when x (the displacement of the 2 kg block) is used as the generalized coordinate. b- Derive the equation of motion of the system in terms of equivalent system parameters (equivalent mass, equivalent spring stiffness and equivalent damping coefficient). 3000 N/m 2 kg 200 N.s/m /=0.04 kg-m² r = 10 cm 1000 N/m 1 kg I' 400 N.s/m ialarrow_forwardA System is found to have the following equetion of motion mtJ x+Bkx = 2mg. Determine the natural frequency of oscillation , the system eppective mass position and the System equilibriumarrow_forwardThis problem is an example of critically damped harmonic motion. A mass m = 8 kg is attached to both a spring with spring constant k = 200 N/m and a dash-pot with damping constant c= 80 N-s/m The ball is started in motion with initial position to 9 m and initial velocity vo = -48 m/s. Determine the position function z(t) in meters. r(t) = Graph the function z(t). Now assume the mass is set in motion with the same initial position and velocity, but with the dashpot disconnected (so c = 0). Solve the resulting differential equation to find the position function u(t). In this case the position function u(t) can be written as u(t)= Cocos (wotao). Determine Co, wo and co S 38 E Co= Wo= (assume 0 do < 2π) Finally, graph both function z(t) and u(t) in the same window to illustrate the effect of damping. α0 =arrow_forward
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