Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 19.5, Problem 19.143P
(a)
To determine
The combined spring constant (k).
(b)
To determine
The damping factor
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A three-blade wind turbine used for research is supported on a shaft so that it is free to rotate about O. One technique to determine the centroidal mass moment of inertia of an object is to place a known weight at a known distance from the axis of rotation and to measure the frequency of oscillations after releasing it from rest with a small initial angle. In this case, a weight of Wadd = 50 lb is attached to one of the blades at a distance R = 20 ft from the axis of rotation. Knowing that when the blade with the added weight is displaced slightly from the vertical axis, and the system is found to have a period of 7.6 s, determine the centroidal mass moment of inertia of the three-blade rotor.
As shown in the Fig. 3, the CM of a cylinder of mass m and radius R is connected to the top of hoop of mass m by a spring. The spring constant is assumed to be known and it is denoted by k. At a given moment the system is slightly compressed and then suddenly released. After the release, both rigid objects roll without slipping. Determine the angular frequency of the resulting oscillation. It is assumed that the spring remains horizontal throughout the motion. Figure 3: Coupled Oscillator
2. A point mass m is strung on a vertical ring of radius R, and it oscillates freely with respect to its equilibrium point
located at the lowest point of the ring. An external moment of force is applied that causes the ring to oscillate about
its center in the form
α = α₁ cost
where a is the angle of rotation. Determine the general movement of the mass m, and under what circumstances this
movement enters into resonance, detailing this phenomenon.
Chapter 19 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 19.1 - A particle moves in simple harmonic motion....Ch. 19.1 - Prob. 19.2PCh. 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 - Prob. 19.8PCh. 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 - Prob. 19.37PCh. 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 - Prob. 19.42PCh. 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 - Prob. 19.61PCh. 19.2 - Prob. 19.62PCh. 19.2 - Prob. 19.63PCh. 19.2 - Prob. 19.64PCh. 19.2 - 19.65 A 5-kg uniform rod CD of length l = 0.7 m is...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 - Prob. 19.78PCh. 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 - Prob. 19.85PCh. 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 - Prob. 19.103PCh. 19.4 - Prob. 19.104PCh. 19.4 - Prob. 19.105PCh. 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 - Prob. 19.112PCh. 19.4 - Prob. 19.113PCh. 19.4 - Prob. 19.114PCh. 19.4 - Prob. 19.115PCh. 19.4 - Prob. 19.116PCh. 19.4 - Prob. 19.117PCh. 19.4 - Prob. 19.118PCh. 19.4 - Prob. 19.119PCh. 19.4 - Prob. 19.120PCh. 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 - Prob. 19.139PCh. 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 - Prob. 19.145PCh. 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 - Prob. 19.162RPCh. 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
- Problem 5: A helical spring of negligible mass is required to support a mass of 50 kg. The stiffness of the spring is 60 kN/m. The spring and the mass system is displaced vertically by 20 mm below the equilibrium position and then released. Find: 1. the frequency of natural vibration of the system; 2. the velocity and acceleration of the mass when it is 10 mm below the rest position. [Ans. 5.5 Hz; 0.6 m/s; 11.95 m/s²]arrow_forwardA motor that turns at 12,000 rpm is suspended from above by a single spring to isolate the building from its vibration. If the natural frequency of the system is to be one fourth of the vibration frequency, by how many centimeters should the spring extend be-yond its unloaded length when the motor is hung on it?arrow_forwardLarge amplitude of vibration is experienced when an engine having mass (1500 + 2) kg operates at a speed of 1500 rpm. An absorber having stiffness k;equal to 1500 N/m and mass m; is attached to the primary system to absorb the vibration. Find: The magnitude of the mass of the absorber. ii. i. The natural frequencies of the system after the addition of the absorber. The values of the stiffness k; and mass m; of the absorber in order to have the natural frequencies of the two degrees of freedom system 15% away from the forcing frequency.arrow_forward
- Vibrationarrow_forwardThree cylindrical rollers of equal length and material are arranged as shown in end view below. Cylinders 2a and 2B have radius r and cylinder 1 has radius 4r. Their axes are parallel to each other and to that of the fixed concave cylindrical surface, of radius 6r, that supports them. They roll without slip. Assuming no damping and following the steps below, determine the frequency of small free rolling oscillations. For rotation 6, of the cylinder 1, determine the resulting rotation of the lower cylinders. [Hint: Does it look like an epicyclic gear train?] (a) When the upper roller rotates with velocity 6, determine the translational and rotational velocities of the centre of mass of the lower rollers. [Hint: In an epicyclic gear train the centres of these would be supported on the planet carrier.] (b)arrow_forward(a) A mass suspended from a helical spring of stiffness s, is displaced by a distance x from its equilibrium position and allowed to vibrate. Show that the motion is simple harmonic. (b) A vertical helical spring having a stiffness of 1540 N/m is clamped at its upper end and carries a mass of 20 kg attached to the lower end. The mass is displaced vertically through a distance of 120 mm and released. Find : 1. Frequency of oscillation ; 2. Maximum velocity reached; 3. Maximum acceleration; and 4. Maximum value of the inertia force on the mass. (c) A machine of mass 75 kg is mounted on springs and is fitted with a dashpot to damp out vibrations. There are three springs each of stiffness 10 N/mm and it is found that the amplitude of vibration diminishes from 38.4 mm to 6.4 mm in two complete oscillations. Assuming that the damping force varies as the velocity, determine : 1. the resistance of the dashpot at unit velocity; 2. the ratio of the frequency of the damped vibration to the…arrow_forward
- Problem 7: A 2 kg mass is hung from the end of a helical spring and is set vibrating vertically. The mass makes 100 complete oscillations in 55 s. Determine the stiffness of the spring. Also calculate the maximum amplitude of vibration if the mass is not to leave the hook during its motion.arrow_forwardThree cylindrical rollers of equal length and material are arranged as shown in end view below. Cylinders 2A and 2B have radiusr and cylinder 1 has radius 4r. Their axes are parallel to each other and to that of the fixed concave cylindrical surface, of radius 6r, that supports them. They roll without slip. Assuming no damping and following the steps below, determine the frequency of small free rolling oscillations. (a) For rotation 6, of the cylinder 1, determine the resulting rotation of the lower cylinders. [Hint: Does it look like an epicyclic gear train?] When the upper roller rotates with velocity 6, determine the translational and rotational velocities of the centre of mass of the lower rollers. [Hint: In an epicyclic gear train the centres of these would be supported on the planet carrier.] (b) (c) Write an expression for the kinetic energy of the whole system at some instant during the oscillation when the rotational velocity of cylinder 1 is , . (d) Write an expression for…arrow_forwardA sieving machine weighs 6,500 lb, and when operating at full capacity, it exerts a harmonic force on its supports of 700 lb amplitude at 12 Hz. After mounting the machine on spring-type vibration isolators, it was found that m the harmonic force exerted on the supports had been reduced to a 50 lb amplitude. Determine the spring stiffness k of the isolation system.arrow_forward
- A mass of flexible machine part, m, of 10 ×10 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 ×15 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 × 8 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_forwarda. A pump rotor of total mass 350 kg has an unbalanced mass of 10 kg and can be modelled as a single degree of freedom system. It is supported on an elastic foundation which has an equivalent stiffness of 2500 N/m and a damping ratio of 0.15. Vibration measurements show that the rotor vibrates with an amplitude of 10 mm at resonance. i. Calculate the radial location (eccentricity e) of the unbalanced mass. ii. Assuming the damping ratio (C) remains constant, calculate the additional mass that is needs to be added to the rotor uniformly such that the deflection at resonance is reduced by 80%.arrow_forwardA spring oscillates with simple harmonic motion at a frequency of 6.33 Hz when a mass of 3.22 kg is hung from it. Calculate its frequency if only 0.99 kg is hung from it.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