VECTOR MECH. FOR EGR: STATS & DYNAM (LL
12th Edition
ISBN: 9781260663778
Author: BEER
Publisher: MCG
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 19.5, Problem 19.131P
(a)
To determine
Show that the interval of time between a maximum positive displacement and the following maximum negative displacement is
(b)
To determine
Show that the interval of time between two successive zero displacements is
(c)
To determine
Show that the interval of time between a maximum positive displacement and the following zero displacement is greater than
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
An oscillator system without damping has a natural frequency of omega 0 = pi rad/s. Several types of attenuation are given to the system to provide a damping factor (y) of 0.1, 0.5 and 1 s^-1. (a) For each damping factor value, determine the omega value of the oscillator!. (b) determine the displacement at time t = 2 seconds for the damping factor y = 0.5 , if the displacement at t = O is 30 mm and v = 1.5 m/s
In an undamped free vibration of single degree of freedom, the initial displacement and velocity are 0.01 m and 0.50 m/s respectively. The natural frequency is 5 rad/sec. The amplitude of vibration is
What is Logarithmic Decrement in damped vibration?
A heavy machine, weighing 3000 N, is supported on a resilient foundation. The static deflection of the foundation due to the weight of the machine is found to be 7.5 cm. It is observed that the machine vibrates with an amplitude of 1 cm when the base of the foundation is subjected to harmonic oscillation at the undamped natural frequency of the system with an amplitude of 0.25 cm. Find
a. the damping constant of the foundation,
b. the dynamic force amplitude on the base, and
c. the amplitude of the displacement of the machine relative to the base.
Chapter 19 Solutions
VECTOR MECH. FOR EGR: STATS & DYNAM (LL
Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.3PCh. 19.1 - Prob. 19.4PCh. 19.1 - Prob. 19.5PCh. 19.1 - Prob. 19.6PCh. 19.1 - Prob. 19.7PCh. 19.1 - A simple pendulum consisting of a bob attached to...Ch. 19.1 - Prob. 19.9PCh. 19.1 - Prob. 19.10P
Ch. 19.1 - Prob. 19.11PCh. 19.1 - Prob. 19.12PCh. 19.1 - Prob. 19.13PCh. 19.1 - Prob. 19.14PCh. 19.1 - A 5-kg collar C is released from rest in the...Ch. 19.1 - Prob. 19.16PCh. 19.1 - Prob. 19.17PCh. 19.1 - An 11-lb block is attached to the lower end of a...Ch. 19.1 - Block A has a mass m and is supported by the...Ch. 19.1 - A 13.6-kg block is supported by the spring...Ch. 19.1 - Prob. 19.21PCh. 19.1 - 19.21 and 19.22A 50-kg block is supported by the...Ch. 19.1 - Prob. 19.23PCh. 19.1 - The period of vibration of the system shown is...Ch. 19.1 - Prob. 19.25PCh. 19.1 - Prob. 19.26PCh. 19.1 - From mechanics of materials, it is known that for...Ch. 19.1 - From mechanics of materials it is known that when...Ch. 19.1 - Prob. 19.29PCh. 19.1 - Prob. 19.30PCh. 19.1 - If h = 700 mm and d = 500 mm and each spring has a...Ch. 19.1 - Prob. 19.32PCh. 19.1 - Prob. 19.33PCh. 19.1 - Prob. 19.34PCh. 19.1 - Prob. 19.35PCh. 19.1 - Prob. 19.36PCh. 19.2 - The 9-kg uniform rod AB is attached to springs at...Ch. 19.2 - Prob. 19.38PCh. 19.2 - Prob. 19.39PCh. 19.2 - Prob. 19.40PCh. 19.2 - A 15-lb slender rod AB is riveted to a 12-lb...Ch. 19.2 - A 20-lb uniform cylinder can roll without sliding...Ch. 19.2 - A square plate of mass m is held by eight springs,...Ch. 19.2 - Prob. 19.44PCh. 19.2 - Prob. 19.45PCh. 19.2 - A three-blade wind turbine used for research is...Ch. 19.2 - A connecting rod is supported by a knife-edge at...Ch. 19.2 - A semicircular hole is cut in a uniform square...Ch. 19.2 - A uniform disk of radius r = 250 mm is attached at...Ch. 19.2 - A small collar of mass 1 kg is rigidly attached to...Ch. 19.2 - Prob. 19.51PCh. 19.2 - Prob. 19.52PCh. 19.2 - Prob. 19.53PCh. 19.2 - Prob. 19.54PCh. 19.2 - The 8-kg uniform bar AB is hinged at C and is...Ch. 19.2 - Prob. 19.56PCh. 19.2 - Prob. 19.57PCh. 19.2 - Prob. 19.58PCh. 19.2 - Prob. 19.59PCh. 19.2 - Prob. 19.60PCh. 19.2 - Two uniform rods, each of weight W = 24 lb and...Ch. 19.2 - A homogeneous rod of mass per unit length equal to...Ch. 19.2 - Prob. 19.63PCh. 19.2 - Prob. 19.64PCh. 19.2 - A 60-kg uniform circular plate is welded to two...Ch. 19.2 - Prob. 19.66PCh. 19.2 - Prob. 19.67PCh. 19.2 - The centroidal radius of gyration ky of an...Ch. 19.3 - Two blocks each have a mass 1.5 kg and are...Ch. 19.3 - Prob. 19.70PCh. 19.3 - Prob. 19.71PCh. 19.3 - Prob. 19.72PCh. 19.3 - Prob. 19.73PCh. 19.3 - Prob. 19.74PCh. 19.3 - Prob. 19.75PCh. 19.3 - Prob. 19.76PCh. 19.3 - Prob. 19.77PCh. 19.3 - Blade AB of the experimental wind-turbine...Ch. 19.3 - A 15-lb uniform cylinder can roll without sliding...Ch. 19.3 - Prob. 19.80PCh. 19.3 - Prob. 19.81PCh. 19.3 - Prob. 19.82PCh. 19.3 - Prob. 19.83PCh. 19.3 - Prob. 19.84PCh. 19.3 - A homogeneous rod of weight W and length 2l is...Ch. 19.3 - A 10-lb uniform rod CD is welded at C to a shaft...Ch. 19.3 - Prob. 19.87PCh. 19.3 - Prob. 19.88PCh. 19.3 - Prob. 19.89PCh. 19.3 - Prob. 19.90PCh. 19.3 - Prob. 19.91PCh. 19.3 - Prob. 19.92PCh. 19.3 - Prob. 19.93PCh. 19.3 - A uniform rod of length L is supported by a...Ch. 19.3 - Prob. 19.95PCh. 19.3 - Three collars each have a mass m and are connected...Ch. 19.3 - Prob. 19.97PCh. 19.3 - As a submerged body moves through a fluid, the...Ch. 19.4 - A 4-kg collar can slide on a frictionless...Ch. 19.4 - Prob. 19.100PCh. 19.4 - A collar with mass m that slides on a frictionless...Ch. 19.4 - Prob. 19.102PCh. 19.4 - The 1.2-kg bob of a simple pendulum of length l =...Ch. 19.4 - Prob. 19.104PCh. 19.4 - A precision experiment sits on an optical table...Ch. 19.4 - Prob. 19.106PCh. 19.4 - Prob. 19.107PCh. 19.4 - The crude-oil pumping rig shown is driven at 20...Ch. 19.4 - Prob. 19.109PCh. 19.4 - Prob. 19.110PCh. 19.4 - Prob. 19.111PCh. 19.4 - Rod AB is rigidly attached to the frame of a motor...Ch. 19.4 - Prob. 19.113PCh. 19.4 - Prob. 19.114PCh. 19.4 - A motor of weight 100 lb is supported by four...Ch. 19.4 - Prob. 19.116PCh. 19.4 - Prob. 19.117PCh. 19.4 - Prob. 19.118PCh. 19.4 - Prob. 19.119PCh. 19.4 - One of the tail rotor blades of a helicopter has...Ch. 19.4 - Prob. 19.121PCh. 19.4 - Prob. 19.122PCh. 19.4 - Prob. 19.123PCh. 19.4 - Prob. 19.124PCh. 19.4 - A 60-lb disk is attached with an eccentricity e =...Ch. 19.4 - A small trailer and its load have a total mass of...Ch. 19.5 - Prob. 19.127PCh. 19.5 - Prob. 19.128PCh. 19.5 - Prob. 19.129PCh. 19.5 - Prob. 19.130PCh. 19.5 - Prob. 19.131PCh. 19.5 - Prob. 19.132PCh. 19.5 - Prob. 19.133PCh. 19.5 - Prob. 19.134PCh. 19.5 - Prob. 19.135PCh. 19.5 - Prob. 19.136PCh. 19.5 - Prob. 19.137PCh. 19.5 - Prob. 19.138PCh. 19.5 - A machine element weighing 500 lb is supported by...Ch. 19.5 - Prob. 19.140PCh. 19.5 - Prob. 19.141PCh. 19.5 - Prob. 19.142PCh. 19.5 - Prob. 19.143PCh. 19.5 - A 36-lb motor is bolted to a light horizontal beam...Ch. 19.5 - One of the tail rotor blades of a helicopter has...Ch. 19.5 - Prob. 19.146PCh. 19.5 - Prob. 19.147PCh. 19.5 - Prob. 19.148PCh. 19.5 - Prob. 19.149PCh. 19.5 - Prob. 19.150PCh. 19.5 - The suspension of an automobile can be...Ch. 19.5 - Prob. 19.152PCh. 19.5 - Prob. 19.153PCh. 19.5 - Prob. 19.154PCh. 19.5 - 19.155 and 19.156 Draw the electrical analog of...Ch. 19.5 - Prob. 19.156PCh. 19.5 - 19.157 and 19.158Write the differential equations...Ch. 19.5 - 19.157 and 19.158Write the differential equations...Ch. 19 - An automobile wheel-and-tire assembly of total...Ch. 19 - Prob. 19.160RPCh. 19 - Disks A and B weigh 30 lb and 12 lb, respectively,...Ch. 19 - A small trailer and its load have a total mass of...Ch. 19 - A 0.8-lb ball is connected to a paddle by means of...Ch. 19 - Prob. 19.164RPCh. 19 - A 4-lb uniform rod is supported by a pin at O and...Ch. 19 - Prob. 19.166RPCh. 19 - Prob. 19.167RPCh. 19 - A small ball of mass m attached at the midpoint of...Ch. 19 - Prob. 19.169RPCh. 19 - If either a simple or a compound pendulum is used...
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
- An air-conditioning chiller unit weighing 2,000 lb is to be supported by four air springs. Determine the stiffness of the air springs needed such that the natural frequency of vibration of the unit has an average of 7,5 rad/s * O 291.1 Ib/in O 121.0 Ib/in O 15.21 Ib/in O 72.78 Ib/inarrow_forward2. A damped harmonic oscillator consists of a block (m = 2.00 kg), a spring (k = 10.0 N/m), and a damping force (F = –bv). Initially, it oscillates with an amplitude of 25.0 cm; because of the damping, the amplitude falls to three-fourths of this initial value at the completion of four oscillations. (Halliday, Resnick & Walker, 2011) (a) What is the value of b? (b) How much energy has been "lost" during these four oscillations?arrow_forwardA vibrometer with mass 0.86 kg and damping ratio ζ 0.62 is designed to measure vibration in the frequency range ωb = 34.8-84.7 rad/sec. Chose the appropriate stiffness from the given values to guarantee the maximum error will not exceed 2% Note:ZY=r2(1−r2)2+(2rζ)2√ a. 115 N/m b. 367 N/m c. 85 N/m d. 2173 N/m e. 680 N/marrow_forward
- A compact object with a mass of 8.80 kg oscillates at the end of a vertical spring with a spring constant of 1.60 ✕ 104 N/m. The motion is damped by air resistance, and the damping coefficient is b = 3.00 N · s/m. (a) What is the frequency (in Hz) of the damped oscillation? Hz (b) By what percentage does the amplitude of the oscillation decrease in each cycle? % (c) Over what time interval (in s) does the energy of the system drop to 5.00% of its initial value? s (d) What If? The atmosphere of Venus is 50 times thicker than that on Earth. If the effect of air resistance on Venus is represented by b = 150 N · s/m, recalculate the answers for parts (a) to (c) for this system if it is set in motion in the atmosphere of Venus. What is the frequency (in Hz) of the damped oscillations? Hz What is the percentage decrease in amplitude in each cycle? % What is the time interval (in s) for the energy to drop to 5.00% of its initial value? sarrow_forward90/s. Question 2:0 A simplified vibration measuring instrument is used to measure the vertical acceleration of vibrating duct which has a frequency of 10 rad/s. The mass of the meter weighs 1.2 kg, k = 10 N/m. a. The amplitude of the relative motion of the mass is (0.125) mm as recorded by the instrument, find max vertical acceleration of the duct. b. What is the amplitude of the duct vibration?arrow_forwardIn free vibration we experimentally determine the natural frequency of a mass-spring system to be f, = 120.2796 Hz. The results show that decreasing the stiffness of the system by Ak = 592880.1217 N/m, the natural frequency will be decreased by Af, = 31.6418HZ. What is thearrow_forward
- 1. Mass suspended simple harmonic motion (measured from equilibrium position), displacement, velocity, and acceleration are x = 75mm, 450 mm/s, a = -442.5 mm/s^2. Period of Vibration and the amplitude of motion. 2. A uniform of rod of mass m = 3kg is supported by a pin at its midpoint c and is attached to a spring constant k = 120 N/m. If end A is given a small displacement, and released, determine the T of it resulting motion A k = 120 N/m = 3kg m = Barrow_forwardProblem 2.149 & 2.150: Response of Damped System Determine the values of 3, wa, and free-vibration response of the following viscously damped systems when x₁ = 0.1 (m), x = 10 (a) m=10 kg, c=150 (b) m=10 kg, c = 200 (c) m=10 kg, c = 250 N• sec m N sec m N• sec m k = 1,000 k = 1,000 N m N sec m N k = 1,000 ( m :arrow_forwardQUESTION 2 Consider a two-degrees-of-freedom system shown below. k₁ woo kz oooo kz oooo m2 F2 What is the amplitude of vibration of mass 1 oscillating at the input frequency? (This is just another way of asking for the amplitude of the particular solution). The answer must be positive. Use scientific notation with 3 significant figures. Omit units. Use m1 = 1 kg m2 = 1 kg k1 = 127 N/m k2 = 106 N/m k3 = 169 N/m F1 230 cos(1.7t) N F2 = 0.arrow_forward
- An undamped simple harmonic oscillator has mass 2.0 kg and spring constant 50 N/m. The initial displacement from equilibrium (at time t = 0) is 0.30 m and the initial velocity is 2.0 m/s. %3D 1. Determine the angular frequency (in rad/s), the frequency (in Hz), and the period (in s). Determine numerical values (not in terms of .) Determine the displacement in the form x(t) = Acos(mot) + Bsin(@ot). That is, solve for A and B in meters, and write oo in radians per second.arrow_forwardA block attached to a spring, oscillates on a frictionless horizontal surface with a period of 0.45 s. The time needed by the block to move (for the first time) from position x = A to x = -A/2 is: 0.2 sec 0.15 sec 0.05 sec 0.3 sec 0.1 secarrow_forwardA mass of flexible machine part, m, of 10 x 2 kg was observed to vibrate badly at frequency of 10 Hz. The vibration was caused by the application of a harmonic force, F of 10 x 10 N to the flexible part. A judgment was made by a mechanical engineer that the vibration was excessive because the frequency of the harmonic force coincides with the natural frequency of the flexible part. (c) Analyze the mass and stiffness of an absorber that would eliminate vibrations of the flexible part at frequency of 10 Hz, if the amplitude motion of the absorber mass, Xa at 10 Hz was observed to be 0.1 x 9 cm. (d) If the flexible machine part is operated in the speed range of 500 to 750 rpm, justify whether the design of vibration absorber in Q3(c) is safe to be used or not.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 PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering 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