PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 22, Problem 75P
To determine
The spring’s maximum compression.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
A mass weighing 16 pounds stretches a spring 4 feet. The medium offers
a damping force that is numerically equal to 3 times the instantaneous velocity.
The mass is initially released from rest from a point 3 feet above the equilibrium
position.
(a) Find the equation of motion.
(b) Will the mass pass through the equilibrium position? if yes, find the time when
it occurs. Justify your answer.
5. After a mass weighing 10 pounds is attached to a 5-foot spring,the spring measures 7 feet.This mass is removed and replaced with another mass that weighs 8pounds. The entire system isplaced in a medium that offers a damping force that is numerically equal to the instantaneousvelocity.a. Find the equation of motion if the mass is initially released from a point 1/2 foot belowthe equilibrium position with a downward velocity of 1 ft/s.b. Express the equation of motion in the form x(t) = Ae sin[( )t ]
Solve for differential equations undetermined coefficients, do not go to international system
A weight of 3.2Ib stretches a spring 6.4 ft. If the weight is released 3 inches below the equilibrium position with a downward directed speed of 6 ft/s and the mass-spring system is in the middle provides a damping force numerically equal to one fifth of the instantaneous speed, determine the equation of motion if an external force given by f(t) = e-t cos(2t) is also applied to weight.
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
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
- 14. For the system shown to the right, the disk of mass m rolls without slip and z measures the displaccment of the disk from the unstretchcd position of the spring. 3k a) find the cquations of motion; b) if the system is inderdamped, whiat is the frequency of the frec vibrations of this system in terms of the parancters k, с, and m;arrow_forward4. A mass-spring system exhibits a period of 5 s and a measured mass of 20 kg. Calculate the spring stiffness k.arrow_forward8. A spring of 21 cm length reaches 30.8 cm after hanging a mass of 1/4 kilogram on it. The medium through which the mass moves provides a damping force equal to three times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward velocity of 2 m/s. Calculate the time at which the mass reaches its extreme displacement, and what is the position of the mass at that moment? (Use g = 9.8 m/s²) Sol.arrow_forward
- When a tree branch bends, it can be assumed that acts as a spring, i.e there is a restoring force −kx in response to a vertical deflection x. Internal friction of wood provides the dominant cushioning and is independent of the hanging mass, that is, F = −bẋ with b constant. We observe that a monkey of mass m1 hangs from the branch. East monkey oscillates many times, up and down before damping off appreciably, and coming to equilibrium. Then a second monkey of mass m2 hangs from the first monkey, and we observe that the monkeys together also oscillate several times before the branch reaches equilibrium. So the new equilibrium position of the branch is three times larger than with a single monkey. Besides, the energy loss per cycle for a monkey is half that of the loss with two monkeys. Based on these observations, determine the mass of each monkey (m1 and m2) in terms of a elastic constant k of the branch and a friction coefficient of the wood b. (Note: k and b are data)arrow_forwardThe maximum permissible recoil distance of a gun is specified as 0.5 m. If the initial recoil velocity is to be between 8 m/s and 10 m/s, find the mass of the gun and the spring stiffness of the recoil mechanism. Assume that a critically damped dashpot is used in the recoil mechanism and the mass of the gun has to be at least 500 kg.arrow_forwardA mass m is attached to both a spring (with given spring constant k) and a dashpot (with given damping constant c). The mass is set in motion with initial position x0 and initial velocity v0. Find the position function x(t) and determine whether the motion is over-damped, critically damped, or under-damped.arrow_forward
- A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a damping force that is numerically equal to the instantaneous velocity. The mass is initially released from a point 1 foot above the equilibrium position with a downward velocity of 14 ft/s. Determine the time (in s) at which the mass passes through the equilibrium position. (Use g = 32 ft/s? for the acceleration due to gravity.) Find the time (in s) after the mass passes through the equilibrium position at which the mass attains its extreme displacement from the equilibrium position. What is the position (in ft) of the mass at this instant? ftarrow_forwardрис Q2. A railroad bumper (which it is used to stop the railroad car) is designed as a spring in parallel with viscous damping. What is the bumper's damping coefficient such that the system has a damping ration of 1.25 when the bumper is engaged by 20,000 kg railroad car and has a stiffness of 2×10 N/m. The railroad car is traveling at initial speed of 20 m/s when it engages the bumper. What is the time at the maximum deflection occurs when dx/dt=0. brings eacharrow_forwardA weight of 32 pounds is suspended from a spring with a modulus of 5 lb/ft. From equilibrium position, the weight is pulled down 4 inches below and then released. Given that the damping force in pounds is numerically equal to four times the instantaneous velocity, what is the position of the weight after sec.arrow_forward
- e(+) 3r S.E.P. The homogeneous disc with a mass of 4m and radius of 3r is supported at point 0. For small oscillations, find the equations of motion of the two – degree – of – freedom system in terms of the given parameters (k,m,r), and show them in the matrix form. The system is in the static equilibrium position at the instant given. 4m 3 2k Sm Ta(+) 5k Зт wwarrow_forwardA set of scales consists of an instrumented spring from which the mass of the measured object can be deduced, and a damper to reduce oscillations of the readings. The mass of the scales is small and the damper is chosen to give critical damping when a 10-kg object is weighed. If a mass of 20 kg is placed on the scales, what is the damping ratio and how many cycles of vibration will occur before the reading on the scales settles to within 1% of the correct value?arrow_forward(b) A small generator of mass m is supported by four anti- vibration springs to reduce vibration levels being transmitted to the floor. Each spring has a stiffness of k N/m. Draw free body diagrams for: (i) The static equilibrium position for the system (ii) The dynamic case when the mass is displaced downwards by a deflection of x m and released. If the mass of the small generator m is 12 kg and (ii) each spring has a stiffness of 800 N/m and the vibration described as simple harmonic motion, calculate the frequency of vibration in Hz and time period of vibration.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University Press
Mechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSON
Thermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEY
Mechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage Learning
Engineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY